Airline tickets include a "9/11 fee" that funds the TSA. Some people have thrown around an "ATC fee" which doesn't exist but is theoretically possible.
I wonder how difficult it would be to implement a "business jet landing fee" specifically for these kinds of rich-asshole-vacation-spot airports? And it would go directly to the controllers working in these VHCOL vacation towns. I know it's a pipe dream, but really, if you have someone spending $10k a flight to bring their family out to a summer weekend on Nantucket or a ski trip to Eagle County then an extra $200 or whatever isn't that much of an ask.
PS this is from the NetJets (EJA) website: "NetJets programs start at $215,000 for a jet card with 275 days of annual access."
This third-party website claims that a Phenom starts around $8k per flight hour.