zip can solve one of the problems I listed, namely the parallel operations problem, because it has an index at the end of the archive which would facilitate random-access (though because it's at the end you'd have to download it fully before you could parallel-extract -- so it's only partially ideal).
The index at the end of the file is definitely a serious drawback for zipfiles; it privileges the writer over the reader (it makes sense given the hardware limitations at the time). For someone archiving their own stuff that's neither here nor there. For container images, JAR files etc the ratio is lopsided.
I wouldn't say zip can solve all of them though.