the block hash is just a checksum, and shouldn't need to be cryptographically secure
If so, then introduce a given weakness, for example in regtest, and then just write some tests to find out.
My understanding is that a secure hash function is not strictly necessary for mining because any flaw would presumably be exploited by all miners, and that would simply increase the difficulty.
You cannot increase difficulty "ad infinitum". There are cases, where things are so broken, that you need some additional "fix". For example: imagine that you replace regular SHA-256 with just SHA-256, reduced to the first 16 rounds. Then, you would need to change consensus rules, for example into "SHA-256 should give this hash, and SHA-3, applied on the same data, should give a number below given target". Because if you don't, then everyone will exploit that weakness. And there is always a limit, how "weak" you can make something, without making it "totally broken".