It's funny you say that, because those are some of the exact things Eureka is incredible at, while also having strong investigation mechanics that actually encourage engaging with the mystery directly.
Where Call of Cthulhu 7e has 46 skills, which I agree is an absurd mount, Eureka only has 21. For reference, DnD 5e has 18.
Eureka's skills are all distinct enough to not get confused with each other, too; there's no having to differentiate whether your character is trying to use First Aid or Medicine, it's just a Medicine skill in Eureka, which is for anything relating to medicine, like patching up a wound, assessing a corpse, determining what kind of drug a pill is, etc. It's never difficult to determine what skill to use in Eureka.
This is part of what actually equips Eureka characters to investigate; every skill in Eureka has both investigative and non-investigative applications which actually gears the character to be able to uncover clues with the skills of a mundane individual; the Driving skill can be used to drive fast and reckless, or it can be used to identify the make and model of a vehicle. Technology might be used to search the internet for information about a suspect's social media account, or to tell if a water heater is working properly. Firearms can be used to fire a gun as well as determine the caliber of a bullet from the size of the exit wound alone. There is not a single useless skill in Eureka.
A +3 in a skill is considered the best a normal human can achieve. One of my favorite characters I've played, who is just a girl with anxiety, absolutely nothing fantastical, has no skills at +3, but has achieved plenty of incredible things that the more fantastical character she's working with really couldn't.
Failing a roll gives more Investigation Points than succeeding, which can be used to retroactively succeed on previously failed investigative rolls (a Eureka! moment) or to increase the likelihood of victory on a non-investigative roll. Characters with more unique Traits or supernatural Traits need more Investigation Points to do that, giving an edge to more normal, mundane characters.
That might sound complicated, but it really isn't; like any ttrpg, the main gameplay consists of the narrator describing the room, investigators poking around and players asking questions and rolling. It's incredibly smooth in practice and utilizes the format of ttrpgs to great use to create the feeling of investigators investigating.
As for how good mundane investigators are, let me take a second to talk about my favorite investigator I've played, Gwen Wilson.
Gwen is a normal woman; she's anxious, nervous, shy, she's a people-pleaser and has been called a doormat more than once. The closest thing to an incredible skill that she has is a little familiarity with computer programming.
But that people-pleasing gets her places; people are more willing to talk with and be friendly to her than the other investigators, and that helps her get information from them. She's the only one of the three investigators who has gotten into a person's hotel room without using a lock-pick and committing a crime; just politely asking to be let in. she's able to break up fights and de-escalate situations; at one point, she stopped one of her fellow investigators from getting into a fist-fight with someone else, a fight which that investigator certainly would have lost, because she is just a normal 17-year-old girl.
As for 'mental health mechanics', which in games like Call of Cthulhu are fraught with so many dubious ideas of what 'sanity' is, Eureka actually does a good job depicting this sort of genre trope in the form of Composure.
Investigators have a list of fears which the player chooses to place from -3 (horrific) to +3 (ridiculous). When investigators encounter these fears, they roll with a modifier relevant to how much they fear that thing. One investigator might be Horrified of corpses, and will likely lose lots of Composure upon seeing one, while another might simply find it Creepy, and is less likely to lose Composure at all when staring at a dead body.
Investigators will also lose composure from skipping meals and sleep, though they also restore composure by eating three meals a day and getting a full eight hours of sleep. Food costs money, and thus requires a Wealth roll, and skipping sleep can be incredibly useful for buying more time and doing things late at night. There are traits that make investigators more wealthy but reduce other skills, and a trait which reduces the consequences of skipping sleep severely at the cost of never restoring Composure from a good night's sleep.
Investigators can also use the Comfort skill to restore each others' Composure, but not on their self (unless they have the Trait for it, and even then, a -1 Penalty is inflicted.) This isn't an armchair psychologist skill, it's more patting-on-the-back, pep-talk and a hug; an investigator doesn't need to specialize in it to be particularly good at it.
What's important about Composure compared to other games is that it isn't a nebulous 'Sanity'; your character doesn't become a 'gibbering fool' when they hit 0 Composure, they're a stressed person being pushed passed their limit, and that stress will start taking a physical toll on them, though rarely enough to outright kill them from stress alone.
Despite this, players are still encouraged to role-play their character as more stressed at lower Composure, meaning an investigator might do something more reckless and brash than they would at higher Composure. Being at low Composure can actually be a useful tool as well as a horrible detriment the investigators want to avoid.
Over all, Eureka is incredible at what it does without being too complex, encapsulating the genres of detective, noir, urban fantasy, and horror significantly better than Call of Cthulhu.
