There are basically two kinds of systems: one is the stable system, the other is the un-stable system.
The stable system is such a system, when there is a fluctuation, the system will return back to its original state, such as a ball inside a bowl.
The unstable system will be further away from its original state if there is a fluctuation, such as a ball in the top of the hill. The instability will have a increasing growth rate, so that the unstable system cannot controlled.
The old 15pt system is unstable, one is the points for serving, the other is the winner to serve. Imaging if one guy is extremely good at serving, but cannot return any serve. He still can win easily and very quickly if he serves first. He can also lose badly and very quickly if the other player serves first. So the final results will be largely depend on the initial state. If players are good at returning serves better than serving. Then the match will be lasting forever. So in a word, both the playing time and playing results are not controllable, and unfair to each players.
The current 21 point system is a stable system for playing time, because it lets every play count. But it is still unstable for the results because the winner serves forever. As in the 15 pt system, it is typical that one player can win 10 points continuously.
So I suggest in 21 pt system, one player serves 5 times, then switches to the other. After 20:20, one can serve only 1 or 2 times. That will prevent instability grow without limit.
But some people like instability, because it is more unpredictable, then you can use 15 pt system or create your own even more unstable systems.