The US is quite an odd beast when it comes to ID, but as far as I understand, not having a government ID at all is mostly a problem with the lower socioeconomic classes. I don't think the people who put down $100 for a reservation will have quite the same problem.
Even if government ID is out of the question, asking for a credit card with the same name should also work as an alternative for those without a drivers' license or any other form of ID. I don't have any numbers of course, but I suspect there's not a lot of overlap between the groups of people who don't have credit cards or ID and the people who go to these expensive restaurants.
Many other countries (and private airlines) will match your ID with your boarding pass; however, airlines often allow you to change the details on the boarding pass up to the very end, sometimes for a small fee. When the scalpers' customers go through security, their boarding passes match their government ID. If airlines wouldn't allow you to change the name on your ticket the day before your flight, scalpers would probably lose a lot of business, at the cost of minor inconvenience to customers.
Even if government ID is out of the question, asking for a credit card with the same name should also work as an alternative for those without a drivers' license or any other form of ID. I don't have any numbers of course, but I suspect there's not a lot of overlap between the groups of people who don't have credit cards or ID and the people who go to these expensive restaurants.
Many other countries (and private airlines) will match your ID with your boarding pass; however, airlines often allow you to change the details on the boarding pass up to the very end, sometimes for a small fee. When the scalpers' customers go through security, their boarding passes match their government ID. If airlines wouldn't allow you to change the name on your ticket the day before your flight, scalpers would probably lose a lot of business, at the cost of minor inconvenience to customers.