I think I agree with all your points, but I also think we should be doing all we can to encourage all those people who can and want to cycle to do so, and to make it as safe and convenient as possible. That's regardless of whether you "allow" cars to still be used. Improving cycling infrastructure is an action that causes benefits and very little in the way of disadvantages.
Any journey that someone makes on a bicycle means one less car clogging up the road. That's an argument that people make who are militantly against cars, but I think it's completely valid even if you think cars are things that are here to stay and you're OK with that. Car drivers should be looking at the people cycling and silently thanking them for making their drive more pleasant because the roads are less busy. But for that to happen, the bicycles need to be able to go on dedicated cycle ways so that cars don't have to slow down to drive around them.
My commute to work is about 45 minutes on the bus. Or 50 minutes walking - that's how much the buses suck, and they're actually fairly good buses as far as buses go. Or it's a 25 minute cycle. It'd be a 10-15 minute drive if there was no traffic and there was actually somewhere to park, which there isn't.
I did spend about 15 years without a car, cycling everywhere I went. It was great. One time I bought a bulky item, and called a taxi for it. I dumped the item in the taxi, told the driver where to meet me, and cycled home. I made it there before the taxi did - the driver looked well annoyed. But I recognise the cars are useful - I have a car now, and it's great for heading out into the countryside in sparsely populated areas to do some hiking. It'd be unreasonable to expect any public transport out there, and the car will always have a place serving those areas.
So, my argument is that we should be making things better for all, not pitting two views against each other.