I want to agree with you, but if it's my system and my browser reporting my bracket, wouldn't it be trivially easy to inject an http-header with the age I want to report?
And by "trivially easy" I mean "somebody already posted how-to for windows to stackoverflow"
The problem is not that it's hard to cheat (it's easy), the problem is it makes you officially a liar and liable for "illegal app use".
It might not be a problem for you, but some underage kid, who lied about their age, gets addicted to a game with in-game purchases and gets into financial trouble now has no recourse against the company who made the addicting game.
You're trivializing how difficult tampering with OS internals in locked down secure boot environments can be. Just look at the state of Android custom roms. Devices that are years old can be impossible to modify the OS on.