Everyone does deserve to be served. Why? Is it because it's an immutable ethical truth? No. It's because that's our culture. The US is a pretty egalitarian society. It isn't perfect but it's still in our cultural DNA.
A lot of the objection is the issue of slipping the seater a $100. If it was an open auction at the door and everybody had to bid for seats, that would just be the way it is, but in America the act of slipping someone $100 to be seated is basically sneaking out of the egalitarian society into a society of privilege, and the egalitarian among us find that offensive. If you want to buy privilege, which is a perfectly valid thing to do, buy it on the open market, not with bribery.
If everybody engages in bribery, and everybody knows it, the sneaky cheating aspect goes away, though I tend to agree with other posters that this creates a moral hazard. Not being a cultural relativist, I am free to say I believe the egalitarian culture here produces superior results to a culture that accepts bribery routinely. It really does lead fairly directly to things like paying off inspectors to not do the inspections, in a non-trivial percentage of the population.
For instance, maybe the taboo isn't against bribery per se, but against conspicuous displays of wealth--"flashing your cash". For instance, it's taboo to openly discuss one's salary or other financial details. You might think conspicuous consumption is a counterexample, but really it works for this point too--since there's no surefire markers of social class and it's taboo to just go around saying "ha ha, I earn 100 times more money than you", people who want to brag about how rich they are buy really expensive things and make sure everyone notices them. (Similarly, since there's a taboo about exposing certain parts of your body, women who want to brag about how fantastic certain parts of their body are wear tight clothing and cleavagey tops.)
If this trick works universally among high-class restaurants in a certain culture (be it the US, New York City, or whatever), it's indeed a cultural norm to do it--even if the norm requires surreptitiousness.
"I work hard but was laid off from my job. America is all about rewarding people for working hard so I got screwed. Therefore it's OK for me to rob a bank in order to compensate myself for my monetary losses which society owes me."
But I'd like to try to reframe this, to focus on what is lost, and who pays the price.
I value transparency and predictability in (most) transactions; I want shopping to be easy, and so I'd rather pay a non-negotiable $100 for something, versus see a pricetag of $200 that I know is negotiable in the range of 30%-70%. (Admittedly, if we're talking about $100,000, I start being interested in the $200,000 plus haggling).
As such, if I learn that a certain business has a non-transparent cost structure, including this tipping-oriented one, I'm disinclined to shop there. So if I witness you bribing the staff, the business owner loses some of my goodwill (even more if you bribe the staff to cut ahead of me in line), which is a Real Loss for them. I'll acknowledge that perhaps the business owner would rather have the business of the bribing type, for whatever reason (perhaps they're bigger spenders).
I guess my conclusion here is that it is unethical for an employee to accept bribes, if and only if they have been given (explicit or implicit) work direction to not do so.
I don't have much to say about whether it's ethical to bribe them, except of course bribing them for unethical gain (e.g. bypassing safety inspections) would be unethical, and maybe it's unethical to incent someone to behave unethically?