Seems to me the real fix is to take reservations over the phone, not rely on apps and intermediaries to handle stuff that can easily be handled by humans, and move on.
Meanwhile, anyone that cares about this can still delegate it to a human. Call the Amex concierge, "can you get me into FooBar at around 7PM any night next week" and they take care of it. The phone adds no fairness; it opens up a way for middlemen to offer a service that you pay for but that the restaurant never sees.
While maybe a rare situation, software to handle reservations is a great idea. You instantly save one employee's worth of work for a tiny amount of money.
The other option is to only take walk-ins, but then you risk having empty tables when people are tired of waiting in line. I am sure many places have tried walk-in only, only to be disappointed about not making enough money. Restaurants like reservations.
As a customer, I see exactly what all my options are, immediately, and can easily switch days to see what else is available. Needing to manually tell a human what I'm looking for (which I might not even know yet, without seeing all the options), and have them read something off a screen or book to me, is a waste of time.
And for the restaurants, they don't have to pay someone to answer the reservations phone number when they're not open. And they don't have to distract staff from their hospitality duties when the restaurant is open. Also I'm sure all of us have called a restaurant while they're busy, and have had to repeat what we've said to busy, overworked restaurant staff member who can barely hear us on the phone over the din of the restaurant behind them.