I started as a programmer and got an MBA from an ok school (top 20). The combination is very valuable (at least to me) for exactly the reason you cite: the best decisions require wading around in the mucky details.
The MBA gives you a few tools that are helpful, but mainly it's a way to brand yourself and have people give you the benefit of the doubt that you can do things other than strictly build stuff.
I personally think the anti-patterns you describe-- the "do whatever it takes" without having the first idea what that is-- are intellectually dishonest and a sort of management-by-roulette. Sometimes you get lucky and it works out, but I don't know how you'd sleep running things that way.
The MBA gives you a few tools that are helpful, but mainly it's a way to brand yourself and have people give you the benefit of the doubt that you can do things other than strictly build stuff.
I personally think the anti-patterns you describe-- the "do whatever it takes" without having the first idea what that is-- are intellectually dishonest and a sort of management-by-roulette. Sometimes you get lucky and it works out, but I don't know how you'd sleep running things that way.