I agree that if you take "play to win" to mean "play in such a way that you will win future games once your pattern has been established" then your strategy is good. However, the commonly understood interpretation is "play to win this game". Again, I'd compare it to claiming honestly every time you draw mafia. In the long run, it would probably boost your winrate by making you a confirmed townie in the majority of your games. But it's not allowed because you're damaging your chances of winning the game you are playing now.
e: Alternatively there's the "unbreakable meta-promise" where you flip a coin in your town games and make the promise on half of them. That makes you a confirmed townie pretty often without making you too much more suspicious in your scum games, and I think that's another unacceptable meta-trick.
That's not true unless you accept that a majority of people care nothing for other people, which isn't true. The viable solution is to assume that your opponent is nice, until they prove otherwise, in which case you're meant to copy them.
Why?
A player who is Nice can be someone that never shoots.
A player who is Naughty can be someone that always shoots.
Two Naughty players that face each other will only win 33% of the time.
Two Nice players that face each other will win 66% of them time.
A Nice player vs a Naughty player will give the Naughty player a 66% win, and the Nice player will never win.
Two Nice players will continue to be Nice until one turns Naughty. Two Naughty players will continue to be Naughty until one can show the other one that they will play Nice.
In essence, your solution fails, because both players can be Nice and get the same win rate as only one of your Naughty players. You cannot win more by being Naughty than you can be being Nice. All you do is screw over the opponent.
Do you know the type of people that pick this route? They are the kind of people that must destroy the things they cannot have. Lacking empathy.
Your solution is faulty, and your justification comes from your own short-sightedness. Your lack of trust is evident, and it will cause everyone else to not trust you. It's a tragic spiral of defeat.
The proper response is copy your opponent. It will give you the greatest win rate for your situation. If your opponent will shoot, then you must too. If you opponent will not shoot, then you are mutually benefiting each other.
But, in the end, two Nice players will always come out ahead of everyone.