This level of aversion to having to "slum it with the masses" where every last bastion where you might come across a person with a 5 figure income is systemically avoided
So the much the same as those with 5 figure incomes who drive rather than take public transit to avoid the homeless people.
I'm not convinced those people exist. Rather, the people with 5-figure income can afford to take a car, so why would they willingly walk for ten minutes to the nearest bus stop and then spend an hour on two different modes of public transit to go somewhere that takes fifteen minutes by car?
I'm also not convinced that very many people exist who would pay $5k a year to go through a different entrance to the airport just so that they don't interact with anybody who isn't in the six-figure club.
That said, I'll admit that having someone drive me to the gate would be nice, assuming it is efficient. Unfortunately, realistically, it won't be unless they build the private terminal on top of or under the main terminal or otherwise provide a cart path that doesn't interact with pedestrian traffic in the main terminal).
I can only assume that the food would be free and readily available like in an Admiral's club (though I suppose you're paying for it, so not truly free), so having something like this at connecting airports would be great, but far less useful at either endpoint.
If they include prepaid valet service for your car as part of the cost so you can just drive up and they'll whisk you to the gate straight from your car with only a brief stop at the security checkpoint, it could have some value — not enough value to spend an extra fifteen to thirty minutes and fly out of SFO, mind you, but some value.
I can't imagine it being worth $5k a year, though, so what I'd expect is that honeymooners will do it as a once-in-a-lifetime way to be treated like they're important, and all the people with money will continue to do their usual.