Thank you for your follow up post which describes your ideas a lot more clearly. I know it's quite a lot more to type, but if you write like this it is much harder for people to misunderstand what you mean. For me it is important because I am constantly trying to correct misunderstandings about Japanese culture.
I will attempt to answer your questions as best as I can. It is not hard for foreigners to get a job in Japan. There are 2 kinds of jobs: permanent positions from which it is difficult to lose your job and temporary positions which are usually renewed every year.
The first kind of position is hard to get unless you are just graduating from some kind of Japanese school (high school, trade school, university, etc). Even for Japanese people it is extremely difficult to get one of these jobs if you didn't get one right out of school. If you left your job, or were let go then it might be nearly impossible. As such, this kind of job is usually out of reach for most foreigners.
This is not necessarily a problem because there are lots of contract positions available and most foreigners are in Japan for a limited amount of time. Your initial visa is for 1-3 years (mostly depending on how much the government thinks you are at risk for not being able to support yourself if you lose your job). If you maintain your position in your job, my experience has been that the renewal is pretty much a rubber stamp. The last time I renewed it was literally a rubber stamp. The immigration official looked at my application for 10 seconds, asked me if I was still working at the same place and stamped the application -- visa renewed for 3 years!
Immigration without a university degree is quite a bit more difficult (but no more so than any other country I've lived in). I live in Shizuoka prefecture which probably has the highest migrant worker population in Japan, so my experiences may not reflect the whole of Japan. But as long as you can get a visa, there are many, many factory jobs available -- in fact there is a real shortage of workers.
The factories like to work with 1 year contract positions for their workers. This allows them to adjust the work force based on the current economic climate. Most Japanese people would like to have permanent positions, so these contract positions go unfilled for the most part.
There are also positions available for skilled workers who may not have gone to university. A good example are care workers for the elderly. In fact, there are many government programs to bring in workers from outside of the country. Like many "1st world" countries, care workers are underpaid here and since it is a very difficult job, most Japanese people would rather not do it.
So, basically, it is comparatively easy to come to Japan and get a job. In fact, many, many people do come to Japan. They just don't stay. Why?
It is hard to explain without being misunderstood, but I will try. If you are not Japanese, living in Japan is hard. This is not to say that Japanese people are hard on foreigners -- quite the opposite! Japanese people usually go out of their way to be extremely friendly and make exceptions for people who do not know the details about Japanese culture. In fact, it is this which forms most of the problem.
I usually explain Japan as an "inside - outside culture". By this I mean that in Japan people naturally form groups. For example, you have your family. You know the people who are inside your family and who are outside. Japanese people treat people on the inside of a group completely differently than the people on the outside of the group. This is integral to Japanese culture.
Now, you might imagine that this creates discrimination since you would have a group of Japanese people and a group of non-Japanese people, and to some extent this occurs. However, it works quite differently than more foreigners expect. If you are on the inside of a group you have a huge number of rules that you must follow (many of them seemingly arbitrary). You will be scolded if you breach one of these rules. At the extreme, you might even be excluded from the group if you show that you can't follow the rules. I have heard a saying, "If a nail sticks out, hammer it in. If it still sticks out, hammer it in again. If it still sticks out, throw it away". This is a pretty accurate description of what it is like on the inside of a Japanese group.
Outside the group, people are extremely polite and friendly. People will almost always go out of their way to help people outside their group. People are always smiling and say nice things. For people outside the group, you can pretty much always break the rules and get away with it. You don't even need to keep track of the rules at all because you are an outsider. The people on the inside will say, "Oh. They are an outsider. They don't know the rules. Let's forgive them".
Most foreigners, when they first come to Japan, experience being on the outside. It is very, very nice. People are so friendly and welcoming and helpful. Eventually you realize that only some of the people actually want to be nice and friendly. The rest of them are following the arbitrary rule of being friendly to outsiders.
This puts the foreigner, who is not used to Japanese culture, in a very awkward position. They aren't used to being treated so distantly. At first you think you are making lots of friends, but eventually you realize that quite a few of your "friends" are simply tolerating you out of a sense of duty. Many of the smiles are just masks and the kind words are simply repeated mindlessly without any particular intention.
At this point, many foreigners would like to get "inside" and in my experience, it is not difficult at all to get inside a group. Most groups are honestly flattered (and often surprised) that you might want to join them. But then you have to learn all the rules -- and follow them. Foreigners in Japan quickly get used to what has been called the "Gaigin Superpower" -- the ability to do whatever you want because nobody expects a foreigner to know the rules. When you start to get inside a group, though, you must always follow the rules. Any infraction -- whether you knew about the rule before hand or not -- reflects badly on the whole group.
Honestly, I know of only a few foreigners who can deal with it. Especially expats from the US or the UK often find that Japanese culture is at odds with their own moral values. They sometimes try to convince other Japanese people to change their ways and to adopt what they believe is a superior way of living. I have found that those kinds of people tend to get crushed by the sheer momentum of Japanese culture.
I suppose you could say that the above is "quite conservative and a bit `introvert`", but it is quite a bit more complicated than that. Of course my views are coloured by my experiences, but I have met many foreigners working here (both professionals and non-professionals). The people who are successful here all have pretty much the same profile: Are fluent in Japanese, are willing and able to follow arbitrary rules and be polite, try not to change Japanese ways of doing things, are willing to be "inside" several groups with all the downsides that entails.
In my experiences, the vast majority of people in the world are not willing to do those things. This is why they don't stay.
I hope you've found the above interesting. I love living in Japan. For whatever reason I find that I am actually more free here than anywhere else in the world. I am aware, however, that it is the rare foreigner that feels the way I do. I do not think that this is a bad thing, but it definitely hampers immigration.
As for improving career choices for women, I feel that this will happen as a matter of necessity in Japan. Again, it is a strange thing about Japan that most foreigners don't understand. In most parts of the world you fight to establish new ideas. These ideas spread slowly until most of the people have adopted them. In Japan it is completely different. Nothing ever changes in Japan. Everybody does things the way they have always done them. Nobody complains and everybody carries on in the same way. Then one day, somebody makes a decision that something will be done a different way. From that day forward, everybody does it that way. Everybody follows the rules. Nobody complains.
Note: Of course they complain! They just complain to their in-group ;-). Pro tip: If you want to know who your real friends are in Japan, they are the ones complaining to you.
As an example, when I first came to Japan, people used to smoke on the street while going places. Or they used to smoke while waiting for the train. One day these signs came up that said "A cigarette butt is eye level for a child. Let's stop walking and smoking." Now I barely see anyone walking around with a lit cigarette. It is now forbidden to smoke on the train platform and I can't recall ever seeing anyone break the rule.
Someday it will happen. The government will tell industry, "You must keep women working even when they have children because we need more workers". It will just happen -- no debate, no struggle, no (public) complaints.
That's Japan.