A couple reasons restaurants don't do this:
1) Loss of quality control over customer experience. For example they provide a $100 dinner, but the client expects a $200 dinner. That creates bad experience
2) Desire to maintain accessibility on price point (same reasons artists don't charge more for tickets) and perceived inequities of charging extra for reservations
3) Rewarding loyal customers who value the food / brand / hospitality rather than the highest bidder which tends to bring in out-of-towners, Amex centurion card holders, wannabe influencers -- people that don't help create loyalty
There are many other reasons I'm sure as well. Most chefs/GMs/owners I talked to at the time emphasized that they sincerely are not in this for the money, and yes, they like to make a living, but being able to build a community of food lovers who are passionate about their brand is what they really care about. I ended up pivoting to try to build a shift management app soon thereafter...didn't work out but a good entrepreneurship lesson!
[0]https://techcrunch.com/2014/07/03/everyone-seems-mad-at-rese...