I'd thought about this before and my inclination, if I could wave a magic want and have the devs overhaul the ship system, would be to have all ships fairly readily earnable in game. Crafting would allow you to keep lower tier ships up to par although the further the tier is from tier 5, the harder it would be to accomplish.
But what I think should be in the C-Store, instead of refits, are... well... defits.
Y'Know, drop some coin, get the Galaxy at Lt. Maybe some of the console slots are locked from use and the stats get scaled down (and scale up with you).
But I have no real problem with paying for level advantages, whereas I tend to think any endgame advantages should be fairly easy to get if they're going to be sold.
So... No account wide ship unlocks. You can EARN them at max rank fairly easily. And you can pay, per character, to get the ships early.
I think the limited sense of ship progression would be gone.
On the other hand, more options.
On the other hand, T1 Defiant???!?!?!?!
Well, to be honest the ship-switching is mainly a computer game mechanic used to generate a feeling of achievement I don't really get. It's not as if my character would transform from a human to a Deltan when I hit level 11 and to a Betazoid when I hit 21. In the series we saw the captains commanding ONE ship. Except DS9 which had a bunch of runabouts first, then the Defiant and after its destruction another Defiant.
Not mentioning that the tier system in STO doesn't matter. A Miranda can take on a Negh'Var. A Defiant can take on a Negh'Var. Only the level they are scaled to counts.