Burnination is not fine.
I can think of at least two specific examples where the loop tag is more than appropriate:
These questions are actually about loops and loop mechanics, in the exact way that questions with the string tag are about strings, or questions with the array tag are about arrays (and those are probably both tags that equally need as much of a clean-up as loop).
Just because your code uses a loop doesn't mean the tag is appropriate.
Just because your primary concern with your code is about your loops doesn't mean the tag is appropriate.
But the two linked questions are perfect examples of the usefulness of the loop tag. The vast majority of questions tagged loop probably do not need the tag and can be cleaned up rather than burning the tag.
As an alternative suggestion, I propose renaming the tag to loop-mechanics in order to discourage it from being used willy-nilly left and right on all sorts of questions that just happen to have a loop in them, and then we clean the tag up.