^All good points. Another important thing to remember is that very few Starfleet ships are just for one thing, with a few exceptions. Most Starfleet vessels are capable of carrying out scientific, diplomatic, and tactical missions.
Yeah, that's my primary concern with the Galaxy class in the OP. I suppose it's one thing to try and analogize modern warships with Star Trek vessels, but the Galaxy class was initially designed to be one of the most versatile ships in all of Trek -- while modern aircraft carriers are floating cities like the Galaxy class, the Galaxy is much more versatile (medical, scientific, cargo, community, diplomatic, transport, research, exploration etc. etc. ship) that matching her up with any modern warship runs into problems. And I imagine that'll be the same with many other Starfleet vessels like the Intrepid.