One needs to avoid "sloppy cognition". If you are making a mathematical proof to show off and really want to be correct, you still won't make a mistake just as long as you are at least somewhat competent at writing proofs. If you are a programmer and you want your software to work, and inevitably want to believe it'll work, if you are competent and not sloppy in your thought - which you can acquire by training - you won't make extra mistakes just because you want the outcome.

On the other side, if your thinking is sloppy, somehow eliminating motivated cognition won't help you a whole lot. It might marginally decrease the error, in some circumstances when the inference chain is very short and some sense goes through despite the sloppiness.

And of course, on the worst side of sloppy, is the thinking where there is no correct logical pathway from something true to what you're thinking, or all pathways are too computationally expensive to traverse, in which case, you're doomed to nonsense, motivated or not (the best you can do is refrain from making an answer in such circumstances).

edit: TL;DR; : if your thinking style can be affected by 'motivated cognition', it is most likely sloppy enough so that the result is most likely entirely untrustworthy even if you remove the 'motivated cognition' from the equation. Same goes for other biases. No, removal of biases does not give you magical computing superpowers allowing you to answer dramatically harder questions. And the unmotivated sloppiness is still sloppiness.