How to use other ships occasionally...
So, taking into account that the same crew might be unlikely to swap ships regularly, getting upgrades or shiny new models after trading their old ship in...
But as narrator you still have a hankering to try out some other ships...
It seems that the best way to gain the benefits of both worlds is to use a temporary measure to move the crew.
Perhaps the crew discovered an abandoned Starship, and the players are the leaders of the 'skeleton crew' assigned to return this ship to a Starbase. Suddenly you have a built in mystery plot in additikon to whatever else you got, along with a good solid reason why they get to play with a new ship for 1 game.
If you want to go small, use Shuttles or Runabouts from the ships stock. Allowing players to experience 'side missions' (Recon, planetary surveying, diplomatic, etc) anything that a small crew and detour would be suitable but sending the ship too much. This is good for pushing the crews limits, without access to massive offensive/defensive systems or the many devices that make 34th century life easier.
Or they could simply be the biggest fish. So well known that their presence would cause half the problem, thus Starfleet assigns the crew to another ship, from a tramp frieghter, to a cloaked defiant, or simply another starship, less well known, so that they can accomplish a mission without the ships renown getting in the way...
Maybe after a greulling season, their ship is in for repairs. And while that is so, the crew are re-assigned a new ship for shakedown, to keep the experienced crew in the field, and use this experience to test the new ship to its limits before they are re-assigned back to their real ship after repairs?
Any other ways of getting players onto another shipo without smashing up a ship regularly?