Do whatever you want to man. 

But we already got like, dine and dash brutalizing heroes. And one who is so paranoid that just running is assumed to be a sign of villainy.
So the 'Overbearing Zealous Templar' Lawful Good guy is, already there. So if you go about that, you'd have to compete with others for that designation, to be viewed as the strictest dude.

Honestly in my opinion, you'd be better off playing a man like the Supes, one who is genuinely Lawful Good and not an overbearing guy. 

But if you wanna play the 'Overbearing Zealot' type of dude, go for it.