I was skeptical before I tried one, but now I prefer pull saws for most fine woodworking tasks. Pulling tensions the blade, which allows it to be much thinner. If a push saw was that thin, it would take more skill not to bend it in use.
There are advantages to the pull saw, that is why people use them. However there are advantages to the push saw as well. For fine woodworking pull has the advantages you state, for course woodworking push uses more powerful muscles. Today we mostly use power tools for most cases where it powerful muscles matter.
