All air travel should have fuel and emissions tax. Normalize them to commercial airliners. That'll incentivize larger, more efficient plane designs. It'll also punish private jets. Also charge a fee for any planes not at least X% full. Also give discounts and waive fees for planes over X size that service under-served airports.
A bunch of regulations like this should make private planes prohibitively expensive, like 10-20x their current cost. But that's a lot of legislation that huge corporations and billionaires would oppose.