You were presenting skill DCs that would provide a 90% chance of success for an expert.
Correct.
The thing is, a "regular dude" at those levels would have about +3, +4, +5, and +6 (at the low end of each tier): +1 stat, plus proficiency bonus.
No, a "regular dude" would be +0, +0, +0, +0 at those levels.
The fact you are including proficiency bonus (as you youself attribute later) is giving the "regular due" a bonus representing further training in that skill, etc.
So this character would need to roll a 7, a 10, a 13, or a 14 in each respective tier. If you build things to challenge experts, someone who is OK at the thing will be sort of OK at tiers 1 and 2, but incompetent at higher tiers.
Ignoring the above point of your "regular dude" not really being regular.... Those DCs at the (corrected) bonuses you list above:
Tier 1: +3 modifier vs. DC 10 needs 7 or better, so 70%
Tier 2: +4 vs. DC 14 needs 10 or better, so 55%
Tier 3: +6 vs. DC 18 needs 12 or better, so 45%
Tier 4: +7 vs. DC 20 needs 13 or better, so 40%
IMO 40-55% is hardly "incompetent" as you claim. I would say they are definitely competent in Tier 1, and even OK at that other tiers. Even at your numbers for tiers 3 and 4 the percentage only drops 5%, not a huge difference in likelihood of success.
Raw ability scores should be the default for any ability or skill check. Proficiency is a bonus, and should not be expected. A proficient character should expect to be good at that thing, and someone who is an expert should be expected to be awesome at it.
Most raw ability scores are +2 or less. Only the abilities a PC is expected to excel at tend to be above +2. Ability represents no formal or professional training--at best IMO any training attributed to ability is meant to represent the (casual) "hobby" level. That is why "proficiency" (as in actual formal training and/or experience, e.g. "focus") begins at +2. Your "hobby" abilities will be at this level or lower typically. Ability scores above +2 represent a combination of informal training, natural talent, etc.
Seriously, go watch Leverage. Not only will it show you how hypercompetent characters can be awesome at the thing they are awesome at, but also how they can be challenged by things a bit outside their wheelhouse. Plus, it's good for the soul.
Ok, while I love Leverage (I've seen every single episode), those are actually tier 3 and 4 types doing DC 20 "hard" things all the time...like the 90% my numbers above indicate. They do fail occasionally at that DC, and "fail to make progress" or "succeed at a cost" often at DC 25 or higher tasks as well. I mean, come on, if you've seen the show you know success at a cost is just about required at least 2-3 times per episode--the complications are what makes it fun.
