it is not obvious to me that there's been significant improvement in gas engines over the past 20 or 30 years. I don't see a lot of similarly-sized new cars that do better than - or even as good as - my old beater.
It's not obvious to you because you aren't paying attention and looking at all the variables. New cars are different from early 90s cars in two big ways:
1) weight. 1a) crashworthiness: a new car will let you walk away from horrific crashes which your '93 POS will kill you. That alone should get you to dump that old heap. However, that crashworthiness comes at a price: cars are heavier than they used to be, usually by at least 500 pounds. Those 80s econoboxes were really small and light; you can't get anything that light any more. 1b) soundproofness: new cars are much quieter inside than your '93 POS. You're probably deaf now because all the interior noise in that thing. However, again this comes at a cost: the soundproofing adds weight. It used to be that only expensive luxury cars like Mercedes had this stuff, but now even $25k regular cars are super-quiet inside.
2) horsepower. New cars have a LOT more horsepower than your old '93 POS. Even "economy" cars are fast now. Back in the 80s, it was normal for an economy sedan to have 90HP and take 15 seconds to get to 60mph. Not any more; even "economy" cars now have sub-10s 0-60 times, and "regular" sedans can do it in 7-8s, which used to be sports car territory in the 80s-90s. No one wants slow cars any more, and in fact they can be considered dangerous since they can't merge properly. But again, this comes at a price: fuel economy.
New cars with GDI engines have truly impressive fuel-economy numbers these days, being able to push 3200-pound cars around with 200+ HP while still getting 37mpg.