You still can in the US. [0] This exact use case is listed as one of the reasons the US Department of State will issue a second passport book.

[0] https://travel.state.gov/content/travel/en/passports/have-pa...

Israel stopped stamping passports years ago, as I understand it. They give you a separate piece of paper/plastic instead.

There may well be other combinations of countries that justify a person having multiple passports.

Last time I checked (4-5 years ago) this was true for international airports but not all land crossings.

Differs by country, but certainly true some places. Norway for example allows you to apply for a second passport, and the need for a "clean" one is one of the valid reasons you can give.

I meant citizens of the other countries that don't have diplomatic relations trying to go to Israel. They only have one passport and would be in trouble if they visited as their passport would be stamped, thus the scheme of a separate document. Meanwhile, the government buys things from Israel that transit via some nearby country to "simplify imports" through "creative incoterms" and naming and all.