Banks are annoying, but they provide an extremely valuable service (deposit insurance) and interest, which is why people tend to store wealth in banks. Are there any similar institutions for BTC?
You are fixated on deposit insurance. The folks letting lots of cash float in Bitcoin are not using it as a bank. You need to shift your mental thinking from banks. "Investing" in BTC can probably be likened to stocks more than banks.
P.S. The concept of deposit insurances does not hold much meaning with Bitcoin. Deposit insurance applies to banks, which hold on to & handle your money. Bitcoin is money. Now, if a Bank of Bitcoin was founded, because maybe you are afraid your PC will get hacked, and you deposited BTC with them, then deposit insurance would be meaningful.
Banks have deposit insurance because they operate under the fractional reserve system and loan out almost all of their deposits, putting them at risk of failing and losing all your money. Hence FDIC and whatnot.
The bitcoin network doesn't do that, hence no need for FDIC. The apparent risks to the BTC network are that a malicious entity gains control of > 50% of the network's computing power and uses that to illegally modify the blockchain, or the network goes down. The network is so big now that only the largest botnets would have a hope of the former, and it would take a global calamity like a scorched earth world war, asteroid, or EMP from an intense solar flare to accomplish the latter.
