Star Trek was a perfect secularist, socialist, pacifist utopia. Aside from Deep Space Nine, which had a heavy B5 influence, what dreck.
The joke for me was the Battle of Wolf 5 where the Borg cube slaughtered Starfleet. We are told later that in 6 months Starfleet will be rebuilt. What bull ! With the slaughter of trained cadre Starfleet will not be rebuilt for a generation. The Japanese Naval Air arm never recovered from Midway. You can't replace thousands of experienced, trained veterans in 6 months.
37 ships were lost in that battle, so I doubt that was the entire Starfleet.
Sure you could. Let's say there are 100 planets in the Federation and each one has an average of a billion people. After "First Contact", a call goes out to replace the losses that Starfleet took. If a thousandth of a percent of the citizens answer the call, you've got a million new recruits. That's more than enough to restaff the lost ships, especially since the Enterprise is the only one that ever actually does anything. Every other ship seems to be guarding the mail run between Earth and Alpha Centauri.