Israel has had something like five elections in the last three years. Getting a free and fair election is not the challenge.
Having people protest in the street is not, to my knowledge, how elections are initiated in any modern democracy.
Israel is a coalition government with at least a dozen different political parties (including Palestinian/Arab parties), which is why Netanyahu has managed to hold power despite most people disliking him; he is extremely effective at coalition building. Someone who opposes him may accept their party joining his government if their minority party is granted important concessions.
That is also what makes him so dangerous. He seems willing to make a deal with any fringe individuals who can help guarantee his power. The likes of Smotrich and Ben-Gvir, literal right wing terrorists, have been given influential government roles dispite representing just the most radical voting bloc.