Yes, you described how the system works. My critique is that ability scores and skill proficiencies don't have enough of an impact.
If you start bumping Arcana checks to DC 20 so that the clueless Barbarian with -1 can't succeed, the Wizard with +5 will also only have a 30% chance at it. A level 5 Wizard with Arcana proficiency and 18 Intelligence would have 40% chance. Hardly an expert.
It's not a good system. To make skilled characters actually skilled at something, the modifiers should be bigger and they should play more with stuff like Expertise i.e. double proficiency. The gap between the least skilled and most skilled isn't wide enough.
Well, it's your opinion. You don't like it. That's cool.
I'm just trying to help you see that it's not as bad as you think. MOST DC's should NOT be DC 20 or more. A DC 20 should be reserved for a really obscure piece of information.
Let's take an example of your party finds a rare item. Now, in true D&D 5e, you don't just know what the item is exactly. You look at it, and it's an amulet. It is in the shape of a star with a green gemstone in it.
Now, you have a party of 4: Gale, Lae'zel, Dorn the barbarian and Shadowheart.
DM calls for an Arcana roll to identify the item. He says, "The DC is 20." That means that this item is VERY VERY rare. There is VERY little chance that no one but Gale has a chance in Hades of knowing what the item is. They still might have a chance if they even have an Intelligence of 10 (0), but that's only IF they roll a 20.
Meanwhile, this very obscure thing Gale gets a +6. He only needs a 14 or higher. Everyone else, 1 in 20 chance, 5% shot at it (just for the sake of the example, saying they all have Intelligence 0 except Gale). Gale gets a 35% chance of success at knowing a VERY VERY rare item's identity. How might he know about it? He's read lots and lots of books about magic items, while none of the others have.
HOWEVER, there is still a 5% chance that Lae'zel might have at some point in her life run into the item somewhere or heard a story about it or saw a picture of it and someone told her about it, or SOMEthing. It's a slim chance, but allowing her to roll gives her at least a chance, and the 35% chance that Gale has at knowing a very very rare item is a lot better than 5%.
Now, let's go with DC 10 Religion check. This is fairly common knowledge we're talking about now. LOTS of people have potentially heard about these details. Same group. But it's also about Shar. Shadowheart has a +4 Religion (I don't remember if she does, but just for the sake of the example). Gale is not proficient, but he has +3 Intelligence, so he gets a +3. Lae'zel and Dorn get a 0.
Dorn and Lae'zel get a 55% chance of success. Intelligence 10, so what this is saying is that there is a 55% chance that the common, average person has heard something about this. Gale gets a whopping 70% chance of knowing it. Why? Because even though it's Religion, not his strongest field of expertise, the man is quite learned in general and thus has a vast library in his head even of things he's not focused his studies on.
And then there's Shadowheart. She gets +4, but because she's a Sharran Cleric, she should get advantage. This is what she does.
So she doesn't just get a 75% chance of success. She gets advantage besides. Her probability of success is WAY higher because circumstances provide her with an extra boost; advantage.
But let's say it's about Tyr. Well, she still gets 75% chance of success because Religion is a field she's studied in. So, she has some knowledge even about Tyr, who she's not super knowledgeable about.
Now let's say she had Expertise in Religion. +6 now. Whoa! She only needs a 4 or higher to succeed in knowing something fairly common about Tyr because now she's an expert in it. That's 4 or higher, an 85% chance of success. At higher levels, her proficiency might go from +2 to +4, and Expertise would make a typical +4 a +8 Double bonus. So, at higher levels, the true expert shines. A 10 or higher roll now would be no contest. No need to roll for the Expert with +8 Double Proficiency because with a +2 Intelligence bonus, that's a +10 total. That means that fairly common knowledge is automatic to the expert. Only the rare and VERY VERY rare stuff would require a roll for the expert.
Because levels determine who is a true expert and master in something. It's not just whether you are proficient or have expertise in it. Those only illustrate that you are focusing your studies in those areas. As you increase in levels, that's when you see a true difference.
Dorn, the Barbarian at level 10 with Expertise feat in Athletics should have like a +10 Athletics while Gale at level 10 will still only have -1. NOW we're talking some serious gap in skill level.
THAT is how it should be done.
So, if you are breaking down a door and you are simply using your brute strength, an ogre with 20 Strength (+5) and who is proficient with Athletics (+3) would get a +8 to try to smash open a door that is maybe DC 10. What's his chance of success? 2 or higher/ 95% chance. On the flip side, Gale with 8 Strength (-1), would need an 11 or higher/ 50% chance. Both can break down the fairly commonly constructed door, but the ogre has a MUCH more likely chance of success than Gale. Can he still fail? Yes. Maybe he slams his shoulder into the wall when he meant to slam it directly into the door. Maybe he hits his head. Maybe he slips. Who knows. Either way, if he fails and he only needed a 2 or higher, that means SOMEthing went wrong and caused him to flub it up. However, he can try again in 6 seconds and if he doesn't succeed the second time... wow! The gods must be against him.
Shoot! I'd probably even give an ogre advantage on such a roll because he's Large, making it even more likely he'd succeed, but that's, again, circumstance bonus.
