The Hunger Games universe presents that the wealthier districts have special training and volunteers for their tributes ("Careers"). While it certainly seems reasonable that the poorer districts could not support such an effort, it also seems reasonable that they would develop some tactic or strategy to combat such dominance of the wealthier districts.
One plausible method for the disadvantaged defeating the advantaged is through absolute numbers, which also makes sense on an individual level. If you are disadvantaged and want to have any hope of survival, wouldn't you prefer to fight a weaker opponent? Thus defeating the strongest opponents is most beneficial to all weaker opponents.
I have only seen the first three installments of the movies and have not read the books, but it is not clear to me why this strategy was not employed, other than to enhance the story-telling.