Someone had a personal mod that tied weapon use to modded ammunition, which sounds pretty neat to me. On paper, it'd bring a dynamic relationship between missiles, cargo capacity, and give an incentive to bringing more logistics ships. The missiles will still be finite, limited by cargo space and resources.
There'd be a lot of work converting everything, though, since not all missiles mounts work the same. Missile size, how much space they take, how much inventory clutter it would introduce, how to make it so manufacturing/buying them wouldn't suck a new player dry of credits, how AI ships would be affected since they don't actually use inventories. There's also the question on how it affects performance and how it can be integrated with other mods. It definitely won't be a solution as simple as adding a cooldown.
Basically, I talked myself out of this one... this concept is terrible! Cue Statler & Waldorf.