People taking part in such contests would take enjoyment from it, or wouldn't waste their time and effort. Maths is a talent for some, and some simply take enjoyment from being able to solve stuff, so using it in competitions is beneficial for them in terms of enjoyment and increasing knowledge. That in itself is a positive. As for negatives; I think this can only come from someone opposing to math contests, which I personally don't. I believe it comes down to the fact that some people believe entering contests is only a chance to boast about certain skills, but the same could be said for spelling contests, sports matches and anything where someone showcases skills that not everyone necessarily has.
As for whether people should or should not enter math competitions, it depends entirely on the individual and whether or not they want to take part, it shouldn't concern anyone else. If people oppose to it, they don't need to be a part of it at all.