Push processing is not the culprit to blocked shadows. You would
have even more blocked shadows if you didn't push process.  Some
people like blocked shadows (heck, that's the standard way with
di**tal!), some people don't. Color neg films are designed to
give average, usually enough detail in shadows at box speeds.
Some people who want more shadow detail, will overexpose. Some
people, who don't need shadow detail but want higher midtones
(like the sky) to "pop", will underexpose the films.