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.
You're certainly welcome to that opinion but you're trying to overhaul the core of the 5e system. You don't have to like it but d20 IS D&D.
This is not a constructive or helpful comment.
If you actually read and tried to understand what is being discussed, you would know that no one is asking for an unrealistic "overhaul of the 5e system" but rather using mechanics that are already built in said system.
