Also if you gzip the binary version and the json version, the gzipped binary is still going to be much smaller.

Same with csv data, for download size it really pays off to preprocess and pack into arrays of binary structs before compression.

This is part of a bigger class of effects in preprocessing data before compression, it is often surprisingly effective. For example delta coding or columnar format (SoA vs AoS) can yield big improvements depending on data.