It's easy to get led into thinking this is ubiquitous, but it really isn't. Life gets difficult for school children around year 3 min middle school (about grade 9). The long and the short of it is that if you want to get a really top job, then you need to come from a top university, which means that you usually need to come from a top highschool, which means that you must get a good mark on your high school entrance example.
Lately it's gotten even a bit more difficult because you are allowed to apply for only 1 public high school and one private high school (unlike the UK, "public" and "private" refers to what you would normally think -- public is publicly funded and private is privately funded). You can always pay your way into a top school if you have enough money, but generally if you want to get in you need a good result on your entrance exam.
Here's the thing most people don't understand: most students don't care. And by most, I mean about 80%. Only 1/4 of high schools are high performing high schools where students are expected to go on to university. Even with that, most students will prefer to go to a high school that is close to them or where their friends are going. Only a few students choose (or are pushed by their parents) to go to the really top schools.
Even with low level schools, you can still make it to a respectable university. The school I taught in is one of the lowest public schools in the prefecture (one year, due to lack of enrollment, we accepted students who scored 0 on the entrance exam! Seriously, you have to be trying to get zero!) However, we usually sent 4 or 5 students to Nagoya university, which is a decent university. Several of my students when to Shizuoka university too -- which is not a great university, but definitely good enough to get a good job in Shizuoka prefecture.
At low level school, students do not study. I mean, a few study because they like studying, but never once did my students do their homework! Students are carefree, happy and energetic. Compared to the highschools I went to in Canada (I moved around a bit), it is absolutely night and day. It's like comparing prison to a holiday camp.
At high level schools, it's really, really hard work and students stay late to study every day (usually coming home around 8 pm). However, the vast majority of the students like studying! And even if you somehow get pushed into a top level school, every school has a kind of "escape hatch" where you basically decide "academics are not for me -- I'm going to become a factory worker".
This is not to say that there isn't pressure to succeed, but the reputation Japanese schools have is completely undeserved.
And to get to the normal argument: what about suicide rates. We can compare suicide rates by age group in Japan [1] and the US [2]. For Japan under 24 (2014) the number is 1814 (0.0000143 per capita) and for the US (2016) it is 6159 (0.0000190). In other words the US youth suicide rate is about 25% higher than Japan's (Why does Japan have a reputation for high suicide rate? Because older people commit suicide -- it is very rare for young people to do so).
[1] (pdf) https://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=web&c...
[2] (scroll down to table) https://en.wikipedia.org/wiki/Suicide_in_the_United_States