I think a fairly easy fix to implement(but very hard to balance properly) would simply to have the map tier a rare drops in affects the weighting of the mod tiers that drop on it. Basically run T16maps and get a higher chance of better items on average, so rares might start becoming worth looting again.
Another would be to somehow make it so rares that drop can compete with rares that are crafted. Maybe adding various league specific mods to items directly, somehow. That's really one of the big problems, currently for many builds, while you want a rare in x slot, you don't want a dropped rare, you need a specific crafted one because you want one stat that can only be found by crafting(delve crafting especially).
That or elder/shaper items, but it's a lot easier to fish for these mods by using a base then rolling it, than to actually find one in the wild due to the very dilluted pool of affixes for these and the scarcity of the drops even in maps that are affected. Again, adding weighting to map tiering so you get more shaper/elder items at higher tiers would probably alleviate this to an extent. If running a T16 shaper map meant you'd get like a hundred of shaper items(which sounds like a lot, but really isn't that many rares), you'd have at least a fair chance at finding the right bases.
Oh and weight the bases too. Higher map tier, higher bases. So many rares get instantly filtered out just from having a low base.
Basically, make it so rares that drop endgame are actually better so it's not 99.999% trash like currently, but maybe only 99%. Honestly I just filter out all rares after a certain point cause it's just not worth the time picking up anything. I mean picking up rings and shit could be worth it but I just can't even be bothered with these. The fact I don't care much about my wealth past a certain point since I only play one char per league and stuff but still.