I understand that the biggest advantage of pressure fed rockets is far
cheaper (and somewhat smaller, lighter) rocket engines, at the expense of
very heavy tanks that have to withstand 250-300 psi instaead of 20-30 psi
for pump fed rockets.

Now pump fed engines typically run 1400-3600 psi, which adds to their
cost. But why would it not be possible to produce a really cheap pump
with a chamber pressure of 250 psi so that we would have the cost benefits
of a pressure fed vehicle with the lightweight tanks of a pump fed rocket?

-- Larry