I also am in favor of standardized transports for all races. (Except CW and Corsair Eldar, maybe, they could use their transports.)
As has been pointed out already, many races do not have transport ships at all, so there's no point in worrying about it not being fluffy. A tyranid fleet with imperial transports attached is no less fluffy than a tyranid fleet with dedicated transports period, so what's the difference? (It could be more fluffy, maybe they're from a genestealer cult!) Also, making up rules that follow the normal ship rules could be hugely beneficial for some fleets. For example, if the Necron transports follow Necron rules, they're way more durable than a standard transport. Are there going to be fewer of them, or they'll be worth less, or what? How will this be balanced?