In the course of any workday, on the now very rare occasions I find myself thinking about such meta-level junk instead of the math at hand, I remind myself that it is a wasted motion - where a 'wasted motion' is any thought which will, in retrospect if the problem is in fact solved, have not have contributed to having solved the problem.

If you rule out doing anything except X, then you won't get much out of accurately evaluating the plausibility of X. The point of considering likelihood of success is that there are always other options, including cutting one's losses. But to rule out all competing options requires some assessment of their plausibility relative to X.