A typical league bowler can more than likely get away with bowling their performance ball for picking up spares.  The reason for that is that once you know the lane conditions of your local bowling alley they aren't going to change much and you don't have to worry about all of the different oil patterns that professionals are dealing with on a week to week basis.  House alleys usually have a lot of oil in the middle which adds to your ability to utilize your performance ball for spare pick ups.

When professional bowlers use a plastic spare ball it allows them not to worry about the lane conditions.  A plastic spare ball will virtually carry no break and allows for a bowler to just pick their spot and roll their ball.  Whereas, if you were to use a performance ball to pick up spares as a professional you would be dealing with 7,8 or 9 different lane patterns a month or so and those changes in lane conditions change the way the ball is going to break and in turn plays a factor in where you want to roll your ball.  With a plastic spare they have a definitive plan for the points on the lane they are going to throw to depending on the placement of the pins and it's a strategy that they do not have to change according to oil patterns.

The majority of the reasoning behind the professionals bowling with plastic spare balls is performance and the comfort of knowing where you're going to shoot depending on what pins are left standing. However, the other reason is a fairly obvious one that speaks to the monetary needs of the bowlers.  The way the PBA regulations are structured you can have a sponsor's logo on your spare ball.

In conclusion, if you shoot your performance ball when you're attempting to pick up a spare your margin for error is smaller than it would be with a plastic spare ball.