SHA256 is not like the step from 128 bit to 160 bit.
To use an analogy, it's more like the step from 32-bit to 64-bit address space. We quickly ran out of address space with 16-bit computers, we ran out of address space with 32-bit computers at 4GB, that doesn't mean we're going to run out again with 64-bit anytime soon.
SHA256 is not going to be broken by Moore's law computational improvements in our lifetimes. If it's going to get broken, it'll be by some breakthrough cracking method. An attack that could so thoroughly vanquish SHA256 to bring it within computationally tractable range has a good chance of clobbering SHA512 too.
If we see a weakness in SHA256 coming gradually, we can transition to a new hash function after a certain block number. Everyone would have to upgrade their software by that block number. The new software would keep a new hash of all the old blocks to make sure they're not replaced with another block with the same old hash.