This sounds like it might be tremendously valuable, especially if it doesn't have too much dev overhead (either for sending the data or investigating the results).
If you tie the stats to starting a new game, that can get skewed by sandbox games. I sometimes make games just to investigate a mechanic, and abandon it after a few minutes of testing.
On the other hand, if you go by achievements or score at victory, you'd only get numbers on completed games... and lots of games don't get finished.
I think ideally you'd sample at random time intervals (real world, not game clock), as well as upon winning or losing a game.
If something along the lines of ARS hacking sticks around, then I'd probably want to sample that also. If people are consistently hacking an ARS to get ship X instead of ship Y, that suggests candidates for balance reviews. Might be hard to get much data here, and with mods that data might be difficult to interpret, though.
You might want to include a heartfelt 'this really helps our small dev team devote our time wisely' bit in any explanation around the opt-in.