For me personally, the subscription paid off because it got me to go much more regularly - without that financial commitment, I probably would've stayed home more often. So the psychological component counts too, not just the pure price advantage.
To your actual question: The thing is, you really have to do the math for your personal program. Look at which plays interest you, google the individual ticket prices, and compare them with the subscription price. For Munich, it'll probably be the case that a subscription makes sense if you really go 5-6 times a year - but I can't say for sure whether the difference is still as significant as it used to be. The theaters have definitely raised their prices across the board.
One more tip: Some theaters offer tiered subscriptions or have special deals for certain seasons. It's worth checking out the Staatstheater website or calling them - the people there can tell you exactly how much you'd save. Your girlfriend's right that flexibility has value, but if you notice you want to go regularly anyway, you're throwing money away if you always buy individual tickets.