I agree with the "usual" answer, or more generally, "the layer above". We shouldn't expect every file format to roll its own error detection.

If you truly care about detecting bit-flips in a writer process's memory, that's a very niche use-case - and maybe you should wrap your files in PAR2 (or even just a .zip in store mode!).

99% of in-the-wild PNGs are checksummed or cryptographically signed at a layer above the file format (e.g. as part of a signed software package, or served over SSL).

Edit: Furthermore, the PNG image data is already checksummed as part of zlib (with the slightly weaker adler32 checksum), so the second layer of checksumming is mostly redundant.