In my opinion prestige isn't really the equivalent of fame. It's more like political pulling power. For instance, in politics today, there are certain entities that are "famous" everyone knows them. However if push were to come to shove others may not go to bat for them.
Take this to the future. If you are a well known captain, that doesn' t necessarily mean that you get whatever command you want. Even if you have done a lot. You may have Pulled all your favors to get something (spent all your prestige) and thus have no real pulling power left until you go and do something marvelous again to make people stand up and say "Give him what he wants" again.
The problem comes with a lot of other things in the game. Outlandish prestige outcomes from missions that really require little effort (some of which should obviously be MUCH harder). This makes prestige far too easy to come across, and you have, in general, no problem getting what you want in a very small amount of time. You want a Warbird? Sure, put in a little bit of time and you're there.
In a perfect world, I would have liked to have seen all sorts of things act like ships, as far as production and even bidding. Officers, shuttles, etc. It would make prestige more valuable. For instance, why is it that you have to go from starbase to starbase to look at new officers, and then click back and forth on the officer screen to see all the officers that may be at the base? Shouldn't starfleet have a database of available officers that you could pick from and it would mearly take time to "deliver" them to your ship, ala ships. This should also be a bidding process. If Spock or Data were up for grabs, how many captains would be tryin' to pull strings to get them on their ship? (of course this would have to rely on it being VERY hard for your officers to reach the level of those types of officers, while being competent should be fairly standard) Now, that would have added a lot in my opinion. But then again I always felt the officers were halfway done. Why have them be skilled in multiple areas, when you can't switch them to a new position except at a base that has officers available to trade in and out?
Anyhow, we could go on and on about what could have, should have been. I will eventually do a write up of what I would have liked to have seen, what I feel should have been, and what I'd like to see in the future. We now have to figure out just what we can do with what we have been given and hope against hope that it will at least function as it was initially intended and not left in a buggy halfway usable state ala OP.