Israel won't push past the Jordan river. Conversely, it will push all the way up to it if they can. In the south, they'll probably stay inside the line separating Cisjordan and Transjordan Palestine.
I agree with this.
Using OTL population numbers for Israel and the West Bank after the war, Israel should have no trouble keeping its Jewish majority, especially once refugees start pouring in from DP camps and Arab countries.
I'm talking more in the long-term here. Sure, Israel is going to have a solid Jewish majority in 1949 even with the West Bank, but when Arabs are having eight or ten children on average whereas Jews have three or four, one can understand why Israel would become very anxious about the long-run.
In this case, we can expect that a lot of the Arabs who OTL ended up expelled into Jordan will probably be expelled further, and probably some of the Arabs in the West Bank will flee as well, so the "problem" is even less.
Is Israel actually going to expel a lot of West Bank Arabs, though? I mean, I could imagine some overenthusiastic Israeli commander expelling the Arabs of Jericho due to its strategic location, but most of the West Bank is pretty hilly and thus I'm not sure that it would be easy to remove a lot of people from there. In this regard, the West Bank can probably be compared with the Galilee--where a lot of Arabs stayed behind in 1948-1949 and which is also pretty mountainous.
This Times of Israel article mentions how the Israeli government was apparently afraid of putting too many Arabs under Israeli rule in 1948-1949:
https://www.timesofisrael.com/as-trump-era-begins-what-does-israel-actually-want-in-the-west-bank/
"In December 1948, during a lull in the fighting in Israel’s War of Independence, the cabinet ministers of the newly declared Jewish state gathered in Tel Aviv to consider a final military push to expel the Egyptian army from the country’s south and Iraqi troops from the northern West Bank cities of Qalqilya and Tulkarem, both of which lie scarcely nine miles from the Mediterranean coast and form Israel’s perilously narrow coastal waistline just north of Tel Aviv.
During the cabinet meeting, interior minister Yitzhak Gruenbaum phrased a question that has plagued Israelis ever since: Is it wise to take control of territories with large Palestinian populations? Israel’s expansions up to that point in the war were into areas that were either sparsely populated to begin with, or from which Arab populations had largely fled; or into places of such desperate strategic significance, such as Lod and Ramle, that Israeli forces simply expelled some of the Arab residents.
The historian Benny Morris described Gruenbaum’s concern as stemming from the understanding that Israel “could not hold territory packed with Arabs.”
The question returned even more forcefully a few months later, when Yigal Allon, the most successful field commander of the nascent IDF, urged prime minister David Ben-Gurion to order the conquest of the West Bank, an operation he thought could be concluded in a matter of days. This was particularly true after a February ceasefire with Egypt freed up a great deal of Israel’s over 100,000 troops to contend with a Jordanian fighting force in the West Bank of perhaps 12,000. Again Israel’s leaders demurred, and for the same reason: Could a Jewish nation state afford to extend its sovereignty over large non-Jewish populations?
In other words, the West Bank as it is defined today — a distinct territory that is neither Israel nor Jordan — was not, as is commonly believed, forged by Jordanian military success in holding the Israelis at bay in the 1948-49 war. It was created, rather, by the Israeli fear of the consequences that might flow from absorbing large numbers of Palestinians. That concern has not waned in 70 years. It is still the primary argument on both right and left against annexation of the West Bank and for the establishment of a Palestinian state."
For some reason, the Israeli leadership in 1948-1949 doesn't appear to have had a lot of confidence that a lot of West Bank Arabs are going to flee or that Israel was easily capable of expelling a lot of West Bank Arabs.
Of course, there's implications elsewhere. Though there won't be more Palestinians in Jordan ITTL than OTL (in fact, there might even be a little less), they're gonna be angrier than OTL and might well end up successfully deposing the Hashemite monarchy like nearly happened OTL.
Does this trigger an Israeli military intervention into Jordan?