The partners will make more money. The lawyers doing the work will make the same amount of money while dealing with twice as many clients.
The partners won't make more money because their associates will be billing the same number of hours. They'll just be doing so for more clients, which doesn't really do the partners any good (aside from making them feel more powerful because they have lots of clients).
But you are still billing by the hour. 8 hours in a day. Do work for 4 clients or work for 8 clients and get the same amount of money?
There are a few law firms that are heavily automated. But they are mostly larger, class action, pay per result, type law firms vs your standard law firm.
Yeah, I worked with one of those "we get paid if you get paid" firms. Professional, courteous, & every conversation we had was completely to the point. First call was with a receptionist. Spent maybe ~30 minutes talking to the lawyer total. They already optimize not to waste time.
If I charge a fixed rate per hour then the number of clients is irrelevant no? 8 hours of work a day pays the same amount, regardless of how many people it serves.