Note that non anarchist philosophies also struggle with the question of "how do we prevent our system from being taken over by the badguys?" Whether it's monarchists saying "this system works great if the monarch is good but the trick is to make sure a doofus doesn't become monarch", or democracies wondering how we can prevent a demagogue from taking power and abolishing the democracy via popular vote. Even communists have the same problem: whatever administration you set up, how do you prevent it from turning itself into something terrible that's bad for people?

So yes, anarchism doesn't solve it but nothing else does either, IMO.