The cleaning rarely solve pops.My experience (owning a similar number of records) is that cleaning with AIVS Enzymatic removes at least 90% of them... much better than "rarely".
The remainder are probably due to flawed or damaged vinyl. I don't have static problems, so can't speak to how often that's a problem for those who do.
Fully agree with Atmasphere that the phono stage makes a huge difference in the ability to avoid over-amplifying sudden transients.