In 3e, having a +4 modifier (through whatever) meant that you automatically succeeded at easy tasks. In 5e, it does not - you still end up with a 25% chance of failure.
What you're saying, here, is that 3e called a DC 5 easy and 5e calls it a DC 10. That's not really saying much about how bonuses worked in either edition. In both editions, stats give you the same mod, to the same d20 check. The difference is in how those checks scale outside the modifiers. In 3e, a fighter could get a 20 BAB, and a wiz no more than 10 - in 5e, they both top out at +6 proficiency. In 3e a rogue could come up with 24 ranks in each of 8+ skills, while a fighter trying to cross class some the same skills would manage 12 ranks in 2 of them - in 5e, the rogue gets more skills than the fighter, and can manage a +12 proficiency in some to the fighter's +6. That's bounded accuracy and it base leaves stats a more important consideration.
In 3e, you could enter a more dangerous situation knowing that your stat meant you weren't actually taking a risk. In 5e, you're going to die pretty quickly doing that.
Out of the lowest levels, 5e gets moderately forgiving. Relatively few SoDs, monsters aren't too overwhelming, deaths saves. 3e could be brutal, not just the SoDs, damage could go off the rails, too.
So your stats changed what was mundane for your character.
In 5e, they don't - they just bump the numbers about by a few percent.
The range of plausible stats is mostly narrower in 5e. 8-20, mostly. In 3e you could, through stacking bonuses get much higher stats, and it was expected, via buffing, wealth/level, & make buy.
This is very true, and unfortunately, the D&D fan community at large is extreme resistant to change. 4th Edition really tried to be the next evolution in D&D, the same way 3rd Edition did for AD&D, but the fans rejected it as not feeling like D&D.
3e often felt more like it was riffing off D&D than AD&D, to me, while 4e reminded me a bit of 1e (just a bit: for instance, returning to monsters having different stat blocks and fewer options compared to PCs).
I guess, at bottom, D&D was a fad, and it's having a come-back, and that /must/ depend on a certain level of evoking the game at it's most popular, whether the results are good or bad in an objective sense, that they're familiar can drive success.
This is what I mean. Imagine a fictional world. Now Imagine a character like Conan, imagine a legion of Conans. Imagine if every opponent Conan faught was as strong as he and the only difference between them was gear and a meager +1 to hit from proficiency.
I love Conan, but as things are in 5e he would be just another PC. I understand PCs are exceptional, except they aren't because their foes are just like them +6 to hit d12+4 damage.
Bounded Accuracy does leave less room to differentiate via numbers, true.
1st level PC has 0 experience points. They have skills and proficiencies but they are inexperienced.
They are beginners.
1st level PCs could be, or not, it depends on their background. A soldier background might, like a 1e 1st-level fighter, be a 'veteran' (been in at least one actual battle). The Folk Hero has certainly done something, maybe not a lot, but one specific feat, to get his status. The 5e 'apprentice tier' terminology, though, certainly suggests inexperience.
As I said it is a feeling that soemthing is wrong not imperical fact. What bothers me is homogenous stats. Why are they homogenous? Because it's advantageous to have higher stats. Because the stat bonuses are dramatic and important.
Because there's a limited practical range for stat values. If you take the array or use the point buy variant, the minimum stat is 8. The cap is 20. In-between, only the even numbers make a significant mechanical difference. Mods thus range from -1 to +5. That's not an enormous range.
You could try to maximize the variety of PC stats via a variant chargen method. For instance, if you had 6 players you could generate stats by having 36 cards, six for each stat, each stat having one each of 8, 10, 12, 14, 16, & 18. You could randomly deal out the cards of each among the players. That way, each character has a different score from each & every other character in every stat. They'd have to pick a class to match their stats, of course...
...and, those are really pretty high stats, you'll probably want to skip ASIs. Allow feats, instead.
No, wait, racial bonuses could still produce duplicate stats.