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.
And in neither of them did adding a +1 modifier to an individual check really matter much if you still had to roll ~10 to succeed.
If I make a character from levels 1-4 in 5e, his stat modifier cannot make a difference as to whether he automatically succeeds at an easy task. I can't just say "I don't even need to roll". I can't make a plan and know that an aspect of it that relies on an
easy thing to do is actually going to succeed. If I break the character generation rules and allocate a 20 to a stat, I can still only automatically succeed on that easy task if I play one of 3 classes.
If I make a character from levels 1-4 in 3e, ranks alone will make me succeed at easy tasks. Where I allocate my statistics will determine whether I can automatically succeed at moderate tasks.
Making success at something meaningful automatic is far, far more powerful than simply shifting probabilities from 25% chance of failure to 15% chance of failure.
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.
You're creating a strawman here. Why is the fighter in your original example choosing cross-class skills? The 3e fighter had 2 (+int - oh look, another important non-class stat!) skills at 24. In 3e, that means if he's got a total of +5 other things (like a stat), he's automatically succeeding at heroic tasks, which seems appropriate for a 20th level character.
In 5e, he gets his +6 proficiency, +5 from a secondary stat... and guess what, he can succeed automatically at easy tasks. Yay! Heroic! As soon as he tries something moderate, he fails 20% of the time. Those aren't the sort of odds that you take if the result of failure is death.
Meanwhile the rogue with the same stat automatically succeeds at moderate tasks. Oh, wait, actually the rogue has an always-on take 10, so he actually automatically succeeds at very hard tasks.
5e panics about the possibility that a DM might let someone at high level with a good skill roll do awesome or impossible things so hard that it wrecks the curve at the low end, making skilled characters that are supposed to be the pinnacle of heroics be unable to confidently perform tasks like "noticing 6 drow tailing you in a dwarf city" or "recognise a shrine to a god" or "recognize weak stonework" according to the only real references we have.
And because of that, it doesn't really matter what your stats are, because it only bumps some numbers about a few percent.