The protesters demanded an end to the war and the release of hostages from Gaza, and also called for elections that many hoped would oust Prime Minister Benjamin Netanyahu.
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.
Coalition government offers a greater voice to minority voices, which is often a good thing. FPTP and two party systems are a race to the middle, which often leaves out people, but sometimes succeeds in diminishing extremists.
I'm not really aware of a system that effectively includes minority voices while deminishing extremists, although a robust constitution helps.
Unpopular opinion: Ranked choice is not much better than FPTP. It's basically indistinguishable except in the case that a third party gains enough support to displace another.
The election is almost guaranteed to happen though, all they're protesting over is the timing.
Netanyahu is claiming he wants to wait till the war is over. The protestors are saying that he's just using that to keep himself out of jail.
The longest Netanyahu can draw this struggle out is October 2026. Another election is guaranteed, Netanyahu isn't going to suddenly make himself dictator with his tiny popularity.
Guaranteed until this "war" stretches on and he needs to delay the election because Hamas just launched a new attack and he needs to stay in government to deal with them.