https://www.touristisrael.com/the-israeli-passport-stamp/974...
It used to depend on where you were coming from. When travelling to Israel for work a few years back, my passport (irish citizen) was not stamped, but my colleague's (at the time, a Turkish citizen) was.
No idea why.
And to show how stupid things were--he also had a stamp he had made up to make forged entries on our yellow books. At that time your average joe certainly did not have an up-to-date smallpox shot--but at multiple border crossings they would hit you up for a bribe if you didn't have an up-to-date smallpox shot. Hence fake them. (Even around 2000 which was the last time I had occasion to have anything added to my yellow book there still was no anti-counterfeit protection.)
1) you travel a lot and sometimes may need to mail your passport off to get a pre-travel visa from some consulate, while you are still outside the USA. This way you can send off one passport to get the visa for your next country, while keeping a valid passport with you while you’re abroad.
2) You need to travel between Israel and countries which have laws against visiting Israel (Historically, GCC countries). This way you can always present whichever passport doesn’t have Israel’s entry and exit stamps on it.
I’ve had two valid US passports at the same time, and I’m just a random nobody American.