"In theory one could arbitrarily split the file, and then compress each of the splits and get a speed up that is roughly comparable?" - it could. that's what is

"In theory one could arbitrarily split the file, and then compress each of the splits and get a speed up that is roughly comparable?" - it could. that's what is done, but for LZ type compressor bigger dictionary (e.g. avoiding splits is for the better) - one more reason why there is .tar -> .tgz (or .tbz), while .zip compresses individually. It would be even better if files are arranged in such way that contentwise they are similar one after each other. I'm not compression expert, just average user since the early days of what we used to call it back in the day "solid" compression.