Thank you for the feedback and the kind comments!
We do agree with you on the push mechanic ending up a bit too powerful in the final version of the game. The "battery charge" used for both the push and the missiles was something we added relatively late. Before that there wasn't a limit or cooldown, and the missiles was a bigger focus for us, meaning the push remained largely untested. Your suggestion of the push breaking asteroids is an interesting one, and we'd certainly try that out if we decide to keep developing the game!