I actually had a better thought regarding this.
When you play on someone else's kit, you get to see how someone else does it. You may like it or you may hate it but the experience is certain to be different from how you do things. It may give you ideas that you would never had thought of for future reference. It may make you play differently than you ever have so you're bound to learn something about your playing. It may change your approach or it may not. You may learn to maintain your kit better than you do. You may learn what spare parts you need to have within reach or take the next time you are in the same situation (wing nuts, felts, washers and the nylon sleeve for cymbal stands).
It was probably posted somewhere else on this thread but it is like a box of chocolates so you never really know what you're going to bite into.
In some instances, you may get to use some of your own cymbals, a snare, pedals and throne. Then again, you may not.
You may be looking for something different from what you're doing and not realize it, and this gives you a break from the same-old-same-old, which can revitalize something in your playing.
You may realize how a different drum head makes a drum sound and feel.
Mike