Only relevant if medusas are largely unknown in your campaign, and will only matter until the first gaze attack goes off.
Ill-considered presumption that accurate and expansive information regarding deadly and/or obscure monsters is readily available on your part. Check is relevant because it might inform the players that they can and maybe SHOULD avert their eyes before they start needing to save vs petrification.
Or they could just skip it (a recurring theme in int checks) and go after the big bad himself.
Ignorant presumption that they know who the BBEG is or have other leads. Or that there is no opportunity cost to making use of alternatives.
Here we go, already starting with arbitrary proficiency locking. Also trap detection falls under perception/wisdom so it only applies to if you care about the first two.
Intended meaning - one single check to differentiate the possibilities made per character. No locking involved. Perception/wisdom implies noticing hidden details, not differentiating or inferring information based on function.
Again, traps are wisdom (perception) checks. Int doesn’t help here.
Wrong, as listed in both PHB and DMG. Perception = notice new details; Investigation = drawing conclusions based on existing / already noticed details.
I can dig it up later but I’m pretty sure the section on identifying items stipulates anyone can do so with a sip, which doesn’t activate the effect of the potions. So no, the all int 8 party is quite able to tell what’s being made.
Presumes items present and/or already made which was NOT stated. Intended implication was that they were not - that the character is gathering information based purely on ingredients, retorts, glassware, and other tools or intermediary products.
Probably one of the closest to being legitimate, but only tenuously, since either the player will be in combat and the check doesn’t help (assuming they don’t have the necessary weapons) or it’s noncombat and group research attempts can discover it through volume of rolls. It’s also worth noting that magic items of any stripe bypass the damage immunity, so this check only matters at levels where players don’t have any.
Flat-out wrong. Checks in combat may be useful because they potentially affect tactics - use of particular weapons and/or attacks. Most parties aren't so loaded down with magic items that everyone possesses both magical melee and ranged weapons. Out of combat, you're making an idiotic presumption that 1) research is realistically feasible and that information is available (e.g. DM might decide that research is ineffective outside a library), 2) that research by anyone else would yield the same information.
You mean like insight? Yeah we have that skill already, it’s under wisdom.
Evidently you missed the subtext. Insight doesn't decipher codes.
Assuming you’ve engineered a situation like this that occurs immediately after entering another country (because even 8 int characters are unlikely to not know the royal crest), yet again you can simply have all group members roll for this.
Just like all of us here in the US would recognize all the state flags? Or those in the EU would recognize region-specific flags? Travelers from far off and exotic locations? Yeah...no.
This one is fine aside from arbitrary restrictions on proficiency, but it’s also the most textbook use of history and none of that info is particularly vital.
Both "vital" and its lesser cousin, "solidly useful," are dependent on the specific information - which was not provided. Making this yet another baseless presumption on your part. Noticing a theme here?
This one is chalked up to wizards not being anywhere near clear enough as to the intent and use of investigation vs. perception, but even the basic rules use a hidden door as an example of perception applying. Since wis is vastly more useful than Int, that is going to be the stat used for this more often than not.
Subjective value-judgments aside, there are clear differences in the skill descriptions in spite of some overlap and/or inconsistent use of the two skills in assorted adventures. Naturally YMMV, but how I personally run things would be to give
different information based on what check was used. Perception might discern a draught of air, an oily smudge on the wall, or a suspicious joint/seam in the surroundings. Investigation would identify that as a secret door rather than a trap or mere sign of disturbance.
Would no one else have mentioned this? No captain giving them passage or guard at the gate? I guess this one applies, but it seems more like a temporary gotcha because I’m not sure the PC’s behavior would change much as a result.
Might or might not depending on whether the watch feels the need to inspect
every single individual entering the town, whether the PCs have any familiarity with the area, how long they may have been there, whether the PCs know enough about the local culture to be aware of where laws are posted, and/or how inherently reasonable local law enforcement happens to be.
Arbitrary threshold and not terribly useful. Will probably allow for one better than normal breath weapon before the players adapt to it.
As well as what resistances the creature has. And how the creature behaves. Yes, I'm sure the PCs have prepared properly for dealing with all possible energy types and that an unresisted dragon's breath makes no difference

Arbitrary? Do you imagine that most lawyers would be able to describe how a loudspeaker works? That your average chef would be able to elaborate on the specifics of lung parenchyma? Do you imagine that a fantasy-medieval world with feuding magical wizards, powerful magical beings with vested interests in outsiders NOT learning their secrets, high average mortality rates, and even more complicated physical realities (due to magic) would be any different?
Why is the ‘per character’ even needed here? You get it in one shot or it breaks by your own admission.
Degree of failure.
Volume of rolls problem is still present, since they can just compare answers if they don’t start it. This is assuming of course that the device is nonmagical and they don’t just use identify or other divination magic, or simply shrug and leave.
Obviously, we know the device is unimportant because the PCs can't identify it, right? And surely if the device is magic or partly magic the PCs can just wave their fingers and completely know its entire function without any possible adverse effects because the that's the way most divination spells work and because device is obviously harmless, yes? Or they could just pool their thoughts together, because after losing fingers and suffering other unpleasant effects after repeatedly prodding the device they surely know which of them REALLY understands the thing, right? Did you actually bother thinking...any...of that through?
Basically, half of what you posted is either linked to another, better attribute, or is otherwise bypassed or ignored without significant consequence. None of these options elevate the stat above any of the others, and even if they were good uses in isolation I suspect their frequency would also be a detracting aspect of the comparison.
Hey, you know what? You're free to DM games as you see fit and interpret the rules as you prefer at your table. And that's fine. But a person doesn't have any business proclaiming that the system is broken when they personally choose to make intelligence-based checks worthless at their own table.