Many cities in North America do. The key is the fine for not having a ticket is high enough that you are on average much better off having a ticket. Generally this works out to enough random inspections that the average person is checked once a month, and the fine for not having a ticket works out to the cost of a 3 month pass. The exact numbers are of course subject to debate, but the above should give any city a good starting place they can play with.

IMHO, if you have fare gates they need to be tied into a parent control system so that parents to limit where their kids are allowed to go alone. I've never seen the implemented and the details are important to get right.