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It's very important in the storage of hashed passwords, but not in checking the integrity of files, which is the use case here.

Avalanche effect is a sign of a good hashing algorithms, but not necessarily all of them.

It is very vital in case of SRI indeed, as because SRI also intended to shield from potential MITM somewhere in CDN stack. But SRI is useful in other areas too. For example for really bare version handling and for handling (somewhat) gracefully corrupted cdn responses (including errors, empty responses etc).

For that, avalanche effect is not all that necessary and CRC32 could do an ok job too.

For this purpose, a theoretical CDN-hash that gives an incrementing ID number for every file ever stored in a CDN would work just fine.