We don't have anything to incentivise doing old content beyond the GF daily. Sure, there are mounts etc, but thats all fluff, its not useful!
Rare drops wouldn't be required, they'd just be nice to have. They'd be an incentive to farm all content, not just focus on a small bit of the endgame. You can have rare drops without them being required or even BiS.
In the first part, you're asking that rare drops be made useful so that people will feel some compulsion to farm it, and, in the second, you're saying that they shouldn't be required or BiS even though, unless the gear actually *is* BiS, you're never going to see people farm it or care about it all that much (excepting it being several tiers of better quality than what the normal drops are, such that it's only *slightly* worse than the actual BiS).
You're essentially contradicting yourself here. You're also ignoring the fact that some people actually *do* farm said outdated content for the "useless" fluff benefits. I farmed the living *bejeesus* out of Lost Island to get my Orosquab and Midnight Rakling. I did the same for SM KP and EV until I got my Tirsa Elite (it only took a year of doing it virtually every week to get it on my main...). People farm leveling FPs to get specific shells. Just because it's not mechanically "useful" doesn't mean it's not desired. If anything, it would probably piss off *all kinds* of people that optimize if the only way to get (insert useful stat increase here) was to farm the hell out of a piece of old content.
Rare drops with tweaked stats don't make people farm old content when the stats on it are no longer worthwhile (which is what you're pretty much asking for; if the rare drop isn't BiS for a couple tiers above it, then it's not gonna be farmed after that content is over). What makes people farm content that *doesn't* lead to BiS gear is the intangible stuff: mounts, pets, interesting models, etc; stuff that remains relevant when the stats no longer are.