It depends on what you define as a restaurant. Should you be talking about a Chili's, then they will do it no problem. In fact, if you're talking about any place where you go out and eat with people and end up wanting to split the check, it's likely low end enough for it to matter.
In a real dining room, it is considered poor manners largely because the staff are much more task saturated and require more time with each table. Having wait staff tied up for 5-10 minutes creating 7-8 bills and running through the same number of cards or making change really impacts the service.
There's an easier way that people with social skills split the bill. Say two couples are out for dinner. It's more common in a nice place to have either one pickup the bill or one spouse from each couple throw down a card and split it. On the aggregate it balances out. Not many people are that cheap that when they're out with friends, they count every penny.
Dining rooms work much better when staff aren't tied up playing cashier.
I've heard servers say the computer won't let them do it after the order was entered in. This isn't true.
Really? You've personally inspected every computer system that every single restaurant uses across the country? Provide some proof or you should qualify or retract that statement.