Letting customers do this on the phone is a risk to the restaurant, because it relies on two things being true: (1) that you'll show up. Showing up in person is a big one -- many diners in urban areas game reservation slots by overbooking, so no-shows are fact of life; (2) that you will not take more than 45 minutes (or whatever duration that doesn't eat into reservation slots).
If you're already there in-person, it's less risky on the restaurant. Then it falls on staff's knowledge of average dining time (accounting for factors like group size, kitchen turnaround time, etc.). This can be codified in an statistical model, but if you're already there in-person, staff can make a call on whether they can fit you in.
For (1), humans can't make a good decision either, unless you're a regular and staff knows you. In theory, a machine can tap into OpenTable or Tock databases to check your no-show rate, but that data is often noisy and spotty.
That said, a restaurant reservation system only has limited degrees of freedom, so if this is a common exception use case, the algorithm can recognize it and escalate to human to resolve.
If restaurants let you do this today, it's likely that they're doing a coin-flip, knowing that they might lose the bet. If that's the case, algorithms can do slightly better than random -- there are reinforcement learning algorithms that can learn about the flakiness of their clientele over time.
Another way around this is selling tickets or taking reservation deposits, like what Alinea in Chicago does -- a $xx ticket to hold the spot which goes toward the cost of the meal. Nick Kokonas (co-owner of Alinea) did a podcast on this where he said that as soon as they did this, the rate of no-shows fell.