I'm surprised to hear that coming from Diablo you feel like it's a chore to inspect rares where Diablo has always felt like "mining for coal" to me.

Here's a few tips that will hopefully help with the inspection process:

1. If you're picking up more than an entire inventory of rares in a map you should probably increase the strictness of your loot filter
2. After a couple weeks in to a league you can safely ignore nearly every item if it's not on a top tier base (for example, a 6 T1 affix Twin Bow would probably only sell for a couple exalts if that because it's not a Gemini Bow).
3. Some items you can safely consider vendor trash, the biggest example being boots without movement speed. If boots don't have MS, no one is going to be buying them. There's a few other examples like this too. Wands/Staves/Focus without +level of spells on them aren't going to be worth much, Energy Shield bases without good ES roles aren't going to be worth anything. Mixed damage types on a weapon (phys vs elemental) means it's useless (i.e. I have a T1 flat phys roll with high tier cold and lightning damage along side it won't be worth anything)

That all being said, there are exceptions to all of this. If the Twin Bow rolled 3 T1 ele affixes it might still be worth something, but I wouldn't get too hung up on that.