I wonder how they do it in cafes ?... In some they give you a code and that gives you a limited time....
Yes, provided you've you've got a fully featured web-browser to enter the code or use to perform a login. With that assumption a reasonably competent nerd could probably help you do it: you'd need to replace the firmware on your router with DD-WRT, or spend fifty quid on a cheap router to use alongside your existing one and put DD-WRT on that. That's what's called a "captive portal": the first time you visit a webpage you're dumped to an authentication page, you type in a code, and then all the magic happens elsewhere to limit your time, bandwidth, etc. You'd sign up for a service like a Community Hotspot and it'd all be good.
This only works if every session is book-ended with a web-browsing session (to handle "login" and "logout"). If you are willing to have everyone "login" and "logout" using the web browser on their device (and that might open up additional problems, because the browsers on-board games consoles don't have parental control software) then as you say, what you've got is essentially a cafe hotspot (slightly more complex as you actually want per-user authentication, rather than vouchers, but that is supported by the software I've pointed you to).
But I suspect that such a solution wouldn't last more than a few weeks. It's inevitable that people would forget to log out (called away for tea, or whatever) and that would result in allocations being burnt up. The need to have either a keyboard plugged in or mess about with on-screen keyboards would mean that people would use simple passwords, and they would become known to other people in the house. Having to "log off" and "log on" would be very, very irritating. You'd have to "whitelist" other devices on your network that can't or shouldn't do authentication (TV, Internet Radio, your own iPhones, whatever).
I confess, when I replied last night I didn't realise that every modern games console has a reasonable web browser in it. My teenagers don't have consoles at all, because I'm member of the Amish community I think they are vile, so won't have them in the house. So I was assuming you'd have a reasonable number of devices around which you would want to time limit, but which couldn't do per-user login via a browser. Your incredulity prompted me to look in more detail, so I will alter my answer:
If you have a web-browser available in each device your children use, and you are willing to permit them to use it (which might bypass parental controls elsewhere) and enforce a policy of login/logout around each gaming session, then although you'd need a nerd, some nerve and some time spent bedding the solution in, it's possible to do it for probably around fifty quid.