Problem: Some humans are currently suffering. Solution: Destroy the universe.
I would argue that details matter here and there is no valid generalization here. Neither of these are good things, but which is worse will depend on the details, and specifically how you define "good solution" and "bad solution".
Doing the wrong thing for the right reason seems in general to be worse, at least in terms of outcome, than doing the right thing for the wrong reason.
Can you give any examples of where you think this isn't the case?
If you do something right for the wrong reason then you have absolutely nothing to learn from and have made no progress at all at finding the correct solution for the problem at hand.
- the Russian monarchy is bad, let's put a "Communist" dictatorship in place - 1930's German farms can't support its people, let's invade Eastern Europe - modern Britain can't afford to pay for all of the hospitals/schools it needs right now, let's pay the private sector to build them for us, keep paying for them for the next 20 years and then find out that we own none of it - terrorists sometimes communicate on the internet, let's bug everyone's conversations
etc, etc.