The space cost is negligible, but the time cost for the encoder is real. Since most decoders do verify checksums, you can't just skip it. Take fpng[1] as an example, which tries to push the boundaries of PNG encode speed.
> The above benchmarks were made before SSE adler32/crc32 functions were added to the encoder. With 24bpp images and MSVC2022 the encoder is now around 15% faster.
I can't see the total percentage cost of checksums mentioned anywhere on the page, but we can infer that it's at least 15% of the overall CPU time, on platforms without accelerated checksum implementations.