I'm something of a free-market advocate, where a free market exists, so I don't think it's an ethical problem.
I think it's more a matter of how much you want to tick off your users.
Your website is probably intended to attract people. You may be selling something, or you may be relying on advertising revenue, or you may just want to create a community. If you don't care if people come, it would be a lot easier and cheaper to create no site, and save on development and hosting costs.
Let the users supply their own passwords, and they're likely to remember them. Issue them, and lots of them will either not write it down, or write it down and lose the paper. A lot of those users are going to try to login again, fail, and leave forever. What percentage of users are you willing to lose just because you don't want them to set their own passwords?
There's also the security issue. If my passwords became compromised, I could quickly change all the ones I care about. Except for that one (I don't actually want to specify it). That means that, if somebody gets hold of that password (and I have written it down, since I can't remember it), I can't stop them from getting at my mumble data indefinitely, or until I can get hold of a sysadmin at wherever-it-is. This can have bad results for your user, and either indirect or direct bad results for you.
Of course, if you have some sort of coercive power to make me use your website, then it becomes a matter of ethics, and I'll resent you if you don't let me control my own password.