Whilst the first part of your point is correct IMHO, for the rest Israel has been the very opposite of a force for stability in the region and the non-conditionality of the US’ help has emboldened successive Israeli governments to behave worse and worse thus making the region less stable (one of their main concerns seems to be to stop nations around them from having stable democratic governments) rather than more.
I would say that ACAB and a bunch of very rich Americans with Fascist tendencies who happen to be Jewish and love the ethno-Fascism which is Zionism having bought American Politics (basically doing what Russia wanted to do and, unlike Russia, actually succeeding) is a far better explanation for continued American support of Israel, a theory that much better explains the unconditionality of the American support for Israel than the idea that it’s because of wanting stability in the Middle East.
Absolutelly, American support makes geostrategical sense up to a point. It’s just that we’re well beyond that point and the American support in its current form (weapon shipments, blocking UN resolutions condemning the genocide) doesn’t make sense for geostrategical reasons (both in terms of stability in the Middle East and because it also damages the perception of America all over the World), so it must be something else driving it.