Say you're designing a game, and you want to have some sort of mechanical representation of power. The simplest possible game has one stat: "power", and that stat gets applied to everything related to probability. The higher "power" you have, the higher the chance that you climb a wall, charm a guard, steal a purse, strike an opponent, dodge a hit, etc.
The downside is that fictionally different characters will be mechanically equivalent: a Power-10 wizard and a Power-10 fighter have the same mechanical chance to do all of those things. This can work in same games (FATE Accelerated is really close to this), but feel unsatisfying in others, where we want to represent some characters having specialization. The fighter ought to be better at climbing rocks and the wizard better at deciphering arcane glyphs; not just fictionally but also mechanically.
If we want differentiation, we start partitioning our stats: maybe some checks are related to body and some are related to mind. Then, our fighter can have Body-7 Mind-3 and our wizard has Body-3 Mind-7. Now, the fighter and the wizard are mechanically different, but there's still a lot of nuance available. Should everyone with the same Body score be equally good at climbing rocks as they are at picking pockets?
Maybe you split up Body into Might, Finesse, and Hardiness, and maybe you split up Mind into Memory, Calculation, and Emotion.
Now, you can mechanically represent characters that are good weight lifters (high Might) but bad pick pockets (low Finesse), or characters that are gifted mathematicians (high Calculation) but poor at geography (low Memory).
Most games go further, making more and more proficiency splits. Every time you do this, you increase the unique number of mechanical representations. If you only have finesse, you're equally good at picking pockets as you are at balancing on a tightrope. If you make a thievery skill, you're equally good at picking pockets as you are at sleight of hand.
That's the upside. You gain more and more unique mechanical representations. It also feels closer to reality.
A downside is that if there's an opportunity cost to allocating this proficiency (limited points to spend in GURPS or Savage Worlds, point buy in d20 systems, allocating rolled stats, limited skill points, limited upgrades when you level up, etc) then the more you split proficiency, the less likely that particular proficiency will come up, and thus the weaker it is. Intuitively, being able to spend 4 points on Thievery will make your character "better" than having to spend 4 points on Pick Pocket, 4 points on Sleight of Hand, and 4 points on Lock Pick. You spend 12 points for the same previous effect as 4, and so you "lose" 8 points that you could have spent elsewhere.
Another downside is that it's higher overhead at the table. Having to remember that Sleight of Hand, Filch, Smuggling, Holdout, and Pickpocket are all splits of Stealing is harder than if there was just a Stealing skill. Having a Stealing skill is harder than calling for a Finesse or Emotion roll, which is harder than calling for a Body or Mind roll, which is harder than calling for a Power roll all the time.
Another downside is that when characters have points, they expect those points to be meaningful. For example, if a character invests into Hiking, then they're attempting to mechanically differentiate based on how quickly they can march over long distances: in a game that has hiking implies that some characters should be able to travel more quickly or for longer than others. You might get down into the minutiae of calculating travel velocity and hours traveled per day, in order to make the investment into/existence of Hiking worthwhile. Is this fun? Or would it be better at the table to just say "ya'll can move X hexes per day"?
Martial characters in GURPS often have high skill in one weapon group (Two-Handed Axe/Mace, for example). Choosing to do this decreases the amount of fun loot (they'll be more likely to be disappointed that they got a magic sword, and not a useful magic axe) and improvisational play that happens.
: We can make a really simple system work by changing the impact based on the fiction. Maybe a success for a Power-10 wizard at leaping over a cliff is that they barely grab the edge of the pit and need help getting up, while failure for the Power-10 fighter is the same as success for the wizard. See Advantage and Impact - Dreaming Dragonslayer
: Personally, I care little about modeling reality. Reality matters less than internal consistency, and way less than making sure the game is fun at the table. If someone is annoyed in a dungeon fantasy game that a character is equally good at mimicing bird sounds as they are at animal sounds because that isn't "realistic"... where does it end?
: A character with DX-13 and 16 Two-Handed Axe mace attacking another character with 9 dodge takes ~3.3 attacks to hit twice. If that character picks up a broadsword and attacks the same opponent, it takes ~12.4 attacks to hit twice, which is a 3.75x increase in number of attacks.