Except there's a difference between overpaying and short term tax minimisation.
I, for instance, in my country, am relatively conservative on my tax returns. I do not push everything out to the point of maximal complexity & maximal returns.
The reason I do this is twofold. If my accountant makes a mistake or a bad call, I am still personally liable for the tax I didn't pay + penalties, even though I sought and obtained professional advice. I know of cases now where people have received "audit shocks" where it turns out the government disagrees with how far they're pushing things, and now they owe money + penalties. Increase that sting and those penalties and watch the risk/return equation change.
The other two reasons are: I pay to support local community and infrastructure. I don't mind paying a bit extra to support public transport in my area, for instance, so if I can find a way to make targeted contributions (as opposed, say, my money going to a contractor in Iraq), then I'll put a bit more in.
And the third reason I don't pay minimal taxes it's a form of social contract/political insurance. I know that if I'm a total prick, or want to do things in the future, if I haven't paid my share, or if someone wants to audit me and go through my books as a political game or to make a point, I have far more political capital and support from the population of I show I'm a good citizen vs "I basically will fuck you all to the maximum extent and screw you". This also provides me a clean conscience, legitimacy, authenticity, and general good will.
Plus if anyone does audit me, for political reasons or otherwise, maybe I'll get a small refund or ruling in my favour, which, at such times, I could really use...