While it would be possible to run a proshop outside a bowling center, it would be a tough way to get started.
Someone with an established reputation would probably do ok. But the extra traffic you get from just being in a center with their league bowlers means a lot in sales. Particularly for wrist braces, rosin, tape, etc.
The real problem comes down to doing a good job. It is often difficult to evaluate a new customer without actually seeing them roll the ball, see the oil lines for their track, get a feel for their approach, timing, etc.
The other problem is they don’t generally have a place to try a ball after drilling to see if it is worked out right. And it isn’t right to expect the bowling centers proshop to finish a ball up. The guy selling the ball made the money so they should do the work.
If they had a lane in the shop they could do this but I doubt if they do.