The market should take care of it like it has for every other type of tipping: the fixed wages of the maitre d' would drop to compensate for the expected compensation in bribes. I don't have the data to prove it, but I suspect this has already happened to some extent and the restaurants themselves benefit indirectly from the bribes.
I think the "level playing field" here is an illusion anyway. I can't afford to go to a $375/person restaurant with or without the bribe.
I'm sorry to say your argument is purely theoretical. "The market" resides in economics texts, reality doesn't always conform to it. I grew up in a country where bribery is rampant. It is a nuisance and a drain on everything.
I think the "level playing field" here is an illusion anyway. I can't afford to go to a $375/person restaurant with or without the bribe.