I agree with the idea that the OP is suggesting, which is that shipyards should have some way of making shipbuilding a reality in game.
That being said, I think it should be limited to caps. Limiting fighter production won't be fun for anyone. Secondly, making a system where only a certain amount of capships may be sold in a certain time might lead to problems. Lets say the timer restarts, and all those capships are immediately bought by lolwhutts. Now, if an official faction wants to buy one, or a responsible indie wants to buy one, they are punished for not being as quick as the lolwhutts, and the lolwhutts end up being the only ones representing the factions capship RP.
If there is a suggestion for how such a situation could be avoided, I would support this.
Second thing I would suggest is that factions that control the shipyards can somehow effect the amount of ships produced, and that they could somehow profit off of it.