I don't think that making a luxury service more expensive will discourage use, unless we can make each flight cost tens of thousands of dollars.
I'd rather just ban assholery than create a steep asshole tax. It doesn't bother me that a few rich people will have to wait in traffic like everyone else (or better - stop traveling for cross-town meetings and take a phone call!).
The point isn't to discourage use per se. The point is to force the entity producing negative externalities to pay for the damages they are incurring. If the business is still economical to run after these costs, it should be run, and the money can be kept to reduce taxes, pay for other noise abatement, etc.
If it's agreed that the behavior is damaging, why allow it? If you take the slippery slope down, then you could simply pay off any negative behavior like rape or murder.
The slipper slope goes in the opposite direction too. All behavior causes damages (negative externalities) to someone somewhere, but we don't outlaw all behavior.
There is a pretty well developed theory of econ & law of when it makes sense to have financial penalties and when it makes sense to have criminal penalties. I don't think I could do justice to it in this comment box, but suffice it to say, "only criminal penalties, no financial ones" is wrong.
You don't know what is and is not economical. Pick a price that will reduce average taxes on affected citizens enough that they are indifferent if the flights occur or not. If that price is too high to make the business economical, it will not occur, which is economically efficient.
Should we place a tax on murder? Certainly there's a payoff at which point, 50% of the voters will shrug their shoulders, and say: "Well, if someone's willing to pay 5 million dollars to want someone dead, surely they've got a great reason to... My property taxes just went down by half a percentage point!"
Suppose that there is a helicopter overhead that you (and the five thousand people around you) would pay a dollar to get rid of. If you tax that flight $5000 and distribute it to the 5000 people who could hear that helicopter, then you get that dollar and you're just as happy as if that flight didn't exist. If you tax that flight $10,000, and distribute it to the 5000 people, then you get two dollars, making you happier than in the scenario where the flight didn't take place.
Obviously, it's impossible to give that money to the people who heard the helicopter, but if you amortize all the flights in the area (say, all of LA) over all the people who live there, and reduce their taxes by that amount, then financially it works out the same. That still leaves some problems (complexity in setting a new tax on helicopter flights, differing value on not-having-helicopter-flights, difficulty of estimation, and so on), and many people want to discourage the mentality of "you can throw money at a problem to get rid of it", but conceptually it seems plausible for taxing the flight to be better than banning it entirely.
This misses the differential impact of the disruption on different people. Freelancers that do audio recording, for example, may need to throw out and redo some of their work when it gets interrupted by a helicopter flyby. You either need to identify these people and five them a higher proportion of the tax revues to compensate, or price your tax/redistribution high enough that these high-value individuals are fairly compensated.
I'd rather just ban assholery than create a steep asshole tax. It doesn't bother me that a few rich people will have to wait in traffic like everyone else (or better - stop traveling for cross-town meetings and take a phone call!).
Leave low altitude flight to emergency services.