I'm still using my 2013 N7, and luckily I've never had the sort of issues you describe here. Sure, the touchscreen is a bit slow, but nothing awful. I bought it late - about two years ago now - so that might explain some of this. After the Marshmallow update (hooray, an Android update arriving on time for the N7 2013 LTE!), it's been entirely stable, and slightly quicker than before. By the way, I can't remember ever needing more than two touch points. What applications do you need that for?
Lately, though, I hardly use it - I work from home, so my PC is in constant use any way, and when I'm not near a PC, the drop in browsing speed when using the N7 compared to my phone (Sony Xperia Z2) is significant enough that I often don't bother, even if the 2" screen size difference is huge.The 3GB of RAM in the Z2 really make a difference when keeping a bunch of tabs open in Chrome. Also, remembering to keep a seldom-used tablet charged is a hassle like no other - and switching it off completely means a roughly 1-minute wait to turn on, by which time I've already picked up my phone instead.
I fully support repairing your N7 for a couple of reasons:
1: throwing away an otherwise fully functional piece of hardware is just dumb. Repair, reuse, repurpose, resell. The world has no need of more electronics waste.
2: As you say, there's nothing better out there.The tablets on the market today are mostly awful (although I fully support the move to 4:3 or 3:2 screens), and I very much doubt it'll improve any time soon. The market has devolved into two segments: "premium" (which frequently isn't, but you still have to pay one), and "we don't make a profit on this so we don't give a sh*t."