Push-in Zerks not usually used..because will come out. If you mean push-in grease or oil cups..they're usually just press fit in. After removed..need to be replaced because the necks become crimped. Used the knurl them when re-installing..which tightens the fit again.
When replacing oil or grease cups with Zirks or Alemite fittings..you usually need to thread the holes so the fittings will stay in when popping grease-gun fittings on and off them.
Nowadays...seems like most lubricated bearings and pivots are pre-sealed. When the bushings or bearings go out..you replace whole bearing..et al. I like the old-school fittings better. Seem to last a lot longer when serviced regularly..
Ichi