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.
That doesn't make any sense, because they are already treating Hamas as the legitimate government. Why would they be so reluctant to allow something that would yield the same outcome that they accept today?
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.
Likud are the ones who have been propping up Hamas. I'm sure the US would like them gone, though.