In addition to their limited reach etc, you have to consider that like modern aircraft, quite a bit of the performance of the craft very likely depends heavily on computer programming. Modern fighter aircraft in particular are extremely unstable (because maneuverability depends on instability), and are only flyable by humans because of a lot of interpretation/supplemental control by the flight computer -- not just of the engines, but of actual control surfaces etc.
One can easily imagine that the flight computer is constantly working to interpret the pilot's inputs and turning that into actual control manipulation/engine manipulation to give the pilot a fast, maneuverable platform for firing; in addition, the computer has to manage the additional complexity of shields (which modern aircraft do not).
So an R2 could potentially do quite a bit to affect the performance of an X-Wing by in effect reprogramming it (or adjusting programming parameters) on the fly. Compensating for an overheating or damaged engine, control thruster, or failing shield generator are all things that can be considered "repair" and would result in the X-Wing maintaining maximum combat efficiency better.
This is in addition to the R2's stated purpose of serving as a nav computer; X-Wings don't have a fully capable nav computer built in, they require the droid to calculate hyperspace jumps.