Ok so it's the US and Israel who have prevented further elections.
You keep making this weird leap regarding the legitimacy of Hamas that you don't seem to notice. It's not Hamas preventing elections, it's the US and Israel, and there preventing them because they basically know Hamas will win.
There is no question around the legitimacy of Hamas except in US and Israeli propaganda. The pretense of democracy is the one you are supposing where a people's choice is only valid if it's the one you preferred they make.