Indeed, FDIC is not something that you need in the case of BTC as it's fluid and is not locked to one "bank" / "exchange" / new future entities. It's interoperable between many systems today too.
You can track the bitcoin reserves on exchanges here: https://cryptoquant.com/overview/full/247?window=day
EDIT: For clarity, I was referring to an actual online wallet, a wallet on a website, but it’s not too different to ask the same question about a software wallet on a computer-connected device that does automatic OS or wallet software updates.
Secondly, you can use computer hardware from before even the invention of Bitcoin, and then code the software on that hardware, developing the libraries yourself.
Third, you can use computers simple enough that it’s not feasible to hide any management engine trickery in it.
Fourth, yes, you CAN actually build your own computer, which I’m trying to do. :)
But to further your point, I still haven’t proven to myself the argument that the elliptic curve used by Bitcoin hasn’t been intentionally compromised like the NIST curves were. I take the word of the Internet for granted there... But I suppose I could prove that myself.