The PSP and 3DS titles also had pause. Pause is more likely to be a key feature on "handheld" games since you're more likely to play in "bursts," and the Switch is a handheld" system.

Moreover, as I understand it there are two Monster Hunter dev teams - a primary team that works on the the "mainline" (previously numbered) games that tended to target console, and a secondary "handheld" team that would handle the handheld spinoffs and ports. Rise was developed by the secondary "handheld" team, World and Wilds are being developed by the primary "console" team.

That being said, I'm with you - I like to be able to pause while on a long hunt to go get a drink or take a quick break.

There's also no real reason to pause for inventory purposes in most MH games due to the way the menu and item swap works. Those games are designed to not need to be paused for that stuff. Or at least, not need it as badly. The pause feature is pretty much entirely for a "I have to step away for a moment" scenario, which is still great they put it in there.