Nothing frustrates me more than not being able to pause for no seemingly good reason. I'm playing Wild Hearts right now and even though I never play online I cannot pause for some reason. To simulate pausing, I can turn off the xbox and the quick resume feature makes it look like the game was paused when I turn the console back on.
Other games guilty of this are Fromsoft games: Dark Souls, Elden Ring and so on.
Obviously all of these games have an online component. Not allowing pausing when this component is activated makes sense. But if I am playing completely online why cannot I pause? In Soulslike the worst exploit I can think of is switching equipment on the fly but is that really that bad? When stuff comes up in the middle crucial moments it frustrates me a lot.
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.