We rely on many central authorities because that was the only way to get safety, security, dependability. Governments enforce ownership, banks maintained records. When the systems were created it was the only way, short of physical ownership of all of your money (who wants $100,000 under their bed?).
Blockchains and related technologies offer an alternative. You can have all the same things, but without the need for central authority. That appeals to some people.
The centralized wallets and exchanges are indeed a potential problem, but you can always switch your money elsewhere, choose a different central authority or choose none. And whatever you choose, the underlying system is still free from central authority. No one can control what you own except you.
The problem that I think is overlooked is that central authorities like governments do more than just that small list of things. They offer protection from inflation and deflation. They offer protection from scams (rollback of the transaction, if you will). They can use physical violence (arrest, confinement, and so on) to enforce their central authority. They can enforce, to some degree, that illegal actions aren't occurring using their centrally controlled currencies. Blockchains do not offer that- for better or worse, you decide.