It depends on the players and the DM.
I'm constantly calling for Int checks. Mostly "investigation", but "investigation" is exceptionally broad and can be applied to so many situations.
Research is one example. In my homebrew, the characters often had to hit the libraries. I love making research part of the game. It is the 4th pillar of play for me--or at least an important part of the "exploration" pillar.
Finding clues--I still use perception to notice things, but an investigation is needed to understand what you notice. This can make solving a problem or finding a trap much more collaborative. The cleric notices something unusual and calls over the wizard to come over and look at it.
Traps. Noticing traps is not the same is avoiding or disarming them. Force the investigation checks. Especially at high levels. Passive perception alone is going to have a high-level rogue noticing all but the best-hidden traps. Personally, a trap noticed by passive perception is more a "something doesn't look right." An additional perception check AND investigation check AND thieves tools check may be needed to get through more complex and difficult traps.
Finding loot. Smart foes will take care to hide their loot smartly. Perception should only get you part way there. Investigation is equally important to finding loot. Bring in other skills to help, like stone cunning, carpentry, etc. Even if using passive perception and passive investigation to avoid bogging down the game play, it still gives more important to a well-blended party.
Nature checks are also an important part of my game. Your observant character may notice tracks, but won't know what they are and needs to ask the ranger to examine. I treat survival and nature checks hand-in-hand like I do with perception and investigation. I spent a lot of my youth outdoors, including stints with the Student Conservation Corp, living 4-6 weeks in remote wilderness areas. I'm also a sucker for disaster and survival non-fiction stories (highly recommend No Mercy: True Stories of Disaster, Survival and Brutality, by Eleanor Learmonth, Jenny Tabakoff). Survivors tend to be BOTH smart AND have the mental fortitude to not give up.
To me, Wisdom (Survival) is more about observation and mental fitness. On the one hand, it is the ability to not give up, to not "lose it". On the other hand, I also use it as a kind of "nature perception": you notice the evidence of wildlife and don't overlook potential sources of water or things that may be polluting that water. If you are familiar with the area, perhaps survival is enough. But if you are in a new location--you also need to use your knowledge of nature as well. In particular, I like to reward players who have both survival and nature proficiency by giving them advantage on finding food and avoiding natural perils.
I might also use intelligence to give advantage to other skill checks. For example, if you are just trying to bribe a guard or get someone to like you, then CHA (persuasion) is enough. If, however, you have to publicly debate someone on a complicated topic, if you are "proficient" in Int, that can give an advantage to your persuasion check.
Why not call for an Int save against confusion? Say you are in a debate against a sophist. How do you avoid being made to look dumb? Think of common movie tropes: the nerd who makes the dumb jock look like an idiot, the wholesome country bumpkin who tries to make a difference but is made to look like an idiot by clever, corrupt city politicians. In the civilized world, Intelligence is used as a weapoon more more strength. Why shouldn't that dynamic be used more in our games?
Also, what about games of intellect? So many backgrounds come with various game sets--whether dice, cards, chess sets, but characters can go an entire campaign and not use them. Make them more important to social interactions.
If you ever have to beat death at a game of Chess or bet against a Sicilian when death is on the line, you'll regret making Int your dump stat.
If Int is a dump stat in your group, that's on the DM and the campaign. But for many people that's fine. They want to pound on monsters, not play detective. Just don't mistake that preference as something missing from the game.
