Looking back from 2021, it seems like putting Zion in Palestine caused a lot of instability in the Middle East.

I think this is a claim that, to put it lightly, may not be true at all. I think there's often an overestimation of the effect that this had on the rest of the Middle East. In some ways, it may even have created stability among Arab states themselves to a greater degree because they had a common scapegoat, rather than fighting one another, but my argument for that would go beyond the 20 year rule so I will leave it there.

Sinai seems more religiously significant to Jews than it does to Muslims, it was much less populated, and it would have ensured the Suez Canal would have stayed out of communist hands (if the state of Sinai followed a similar path to Israel).

In other words, why was Palestine chosen over Sinai?

As for "Why Israel", it was because, as I describe in this thread (and u/gingerkid1234's excellent answer is another to read there), the question wasn't just "Where would this be the best for our interests", it was also a matter of "Where are Jews now and what will they want?"

So Israel was placed where Israel is because that's where Jews were, and where Jews were asking and pushing for statehood. To get them to the Sinai would have required moving around 600,000 Jews out of the area they'd spent 60 years trying to develop and grow, towards a desert.

Since the UN couldn't even agree on enforcing its partition plan to create a state (so no one "chose" the area for Israel besides Jews, necessarily), the idea that they could have "given" Jews the Sinai would be even more outlandish. The Egyptians were not likely to go along with that theory either, and give up land from their state for a Jewish state they opposed in principle. Jews were not going to fight for the Sinai, when they were already fighting for the land they viewed as their national homeland and native land. Nor was the land particularly great as far as the framework for building a state; the Sinai has always been particularly difficult to patrol and control given its vast deserts and the semi-nomadic nature of many Bedouin who live there. So only by disregarding Jews entirely and effectively ethnically cleansing them from what became Israel could you have gotten them into the Sinai for a state in 1948.

What about earlier?

Well, earlier than 1948 there was at least one proposal for a Jewish state in the Sinai, back when fewer Jews lived in what is now Israel. This was during the period of British control, before the British agreed to try to create a Jewish "national homeland" through the Mandate for Palestine granted formally in the League of Nations in the early 1920s.

Indeed, Jews even heavily considered this only part of the Sinai, around Al-Arish (along the coast and relatively close to Gaza). This was around 1902, and Jews viewed it as a jumping-off point, as Shlomo Avineri puts it in Herzl's Vision. Its proximity was enticing; Jews viewed it as a toehold from which to also enter and create a Jewish state in Israel. So at the end of the day, simply ignoring Jews' wishes was never likely to work; Jews, with their historical reasons and strong desire, were always going to seek a state in what they considered their actual homeland rather than anywhere else.

The considerations about this were extensive and I can get into the details, but suffice to say they began in 1902 or so with British leaders, and ended around 1903. The British were never enthusiastic about the idea, in part because they worried about the geopolitics of it and also the implementability. Still, they agreed to look into a delegation sent to survey the area for possible Jewish settlement and community. Midway through this process, they also made clear that local Egyptians would also have to agree, and since they wouldn't, a full Charter for settlement would not be granted; something less would have to be found. After a Jewish delegation was sent to survey the land nevertheless, and returned a favorable (with caveats) report, the British reacted even less enthusiastically. As they negotiated a contract with Jews to develop and settle areas there, they reached several impasses. For one, they needed way more water than was available for any agricultural or self-sufficiency work, and a pipeline to supply that water (coming from the Nile) would block or interfere with navigation in the Suez Canal for weeks. The British, as mentioned, were never enthusiastic to begin with, and neither were local Egyptians. So eventually, the British denied any request for the area and moved on from that idea. It was only the growth of the Zionist movement, as well as the changes to geopolitical and moral imperatives (and options) after WWI that made a truly bigger impact on British thinking later on and led them to agree to a "national homeland" (though they refrained from saying "state" outright, and danced back and forth on that) for Jews in their Mandate.

Hope that provides you with both a short description of some of the history, as well as some reasons given for actions taken, and I'm happy to talk further if you have more questions!