If your bank’s encryption is broken in the future, then, to recover, you will need to change your password, and that’s all. Bitcoin does not have that luxury.
Also, your bank can switch to securing TLS with post-quantum key exchange algorithms with little difficulty and with no particular scalability or re-architecting challenges.
As for “256-bit”, the best known quantum attack against symmetric ciphers is Grover’s algorithm, and Grover’s algorithm will never break a targeted 256-bit symmetric key in the lifetime of the universe even if run by a hypothetical alien civilization with a Dyson sphere. (It might plausibly break one of many targeted keys in a multi-key attack run by advanced aliens, but this won’t steal your money and it could be easily mitigated by moving to 384 or 512 bits.)
Also, your bank can switch to securing TLS with post-quantum key exchange algorithms with little difficulty and with no particular scalability or re-architecting challenges.
As for “256-bit”, the best known quantum attack against symmetric ciphers is Grover’s algorithm, and Grover’s algorithm will never break a targeted 256-bit symmetric key in the lifetime of the universe even if run by a hypothetical alien civilization with a Dyson sphere. (It might plausibly break one of many targeted keys in a multi-key attack run by advanced aliens, but this won’t steal your money and it could be easily mitigated by moving to 384 or 512 bits.)