CR 3 Ogres might not but if we're talking about CR 15 monster when you are level 20...there's certainly a possibility that they hit more often than some of the CR 20 monsters by having bigger bonuses.
Sure, but they're not 'much lower level,' in 3.5, as you know (but for the benefit of anyone who doesn't), a CR=PC level monster was meant to be a challenge, by itself. A CR -2 monster you could face two of, and it kept doubling per 2 CR lower. So a CR 15 monster is a perfectly reasonable thing to face at level 20 - if there are about a half-dozen of them. It's not 'far below your level,' but an Ogre, for instance, would be - though it is on the lower edge of useable. (Also consider that the PCs, even the melee-oriented ones, at level 20, could easily have a 5- or 10-pt gap in attack bonus, so a 5 level/CR difference could be eclipsed by that, alone.) So, yes, with 'only' a 5 CR difference, the vagaries of the CR system (and PC balance) do make it a toss-up whether it's going to be a real threat or not, able to hit with difficulty or easily. Take it out to 10+ CR differences, though, and even the uncertainty of the CR system is going to be overcome eventually.
The quick and dirty rules said to just add 1 for every level. But the reason it fell apart after about 5 levels is because 1 per level isn't correct(mostly because the extra 13 isn't spread out evenly amongst the levels and comes in bursts).
That's not exactly 'falling apart,' just not an exact 'treadmill.' On occasion you might have an even level where you upgrade an item, and bump a stat from odd to even and get a +3 "in one level," for instance. As with the inconsistency of CR, though, that's drowned out when you're talking a large (say 10+) level disparity, after which you're prettymuch looking for '1's and '20's again. As mentioned above, you can drag monsters back into the ballpark by changing secondary roles while holding exp value constant, but it's a tad unintuitive.
I'd argue that someone who had a 14 in their prime stat is a perfectly viable character in 5e. The difference between a 14 and 20 in their prime stat is significant but it is not enough to make you lose battles unless you are facing very hard monsters.
A 3-point swing is pretty significant. In 3.x, you might get away with it as the stat bonus is 'overwhelmed' by BAB and skill ranks and so forth. In 4e, you'd want to gravitate towards tricks like weapon attacks vs nACDs, effect lines, and outright handing your actions off.
In 5e you could avoid spells that grant saves (or at least, those negated by saves) or be very canny about always forcing your targets' worst saves, but that's seriously cutting into your effectiveness. Fighter multi-attacks would only serve to multiply the effect of the deficiency - though if you ever got Gauntlets of Ogre Power or a Belt of Giant STR you'd suddenly be just fine.
That's a really interesting question, actually. Within the 5E framework, what would be required to make an effective "stat generalist?"
The whole D&D paradigm - class & level, rewarding specialization, managing limited-use resources - seems to be set against it.
It'd be nice if we could build someone like Tanis Half-Elven as a stat generalist: Not as strong as Caramon, not as smart as Raistlin, not as agile as Tasslehoff, not as wise as Goldmoon, just an all-around competent warrior type. Here's a thought:
Versatile Warrior (Feat). Whenever you make an attack roll, increase your ability score bonus on that roll by 2, up to a maximum of +5.
So let's say Caramon and Tanis are 6th-level fighters, who both started with Str 16 and Dex 14. Caramon gets two stat boosts and uses them to pump his Strength to 20. Tanis gets Versatile Warrior and raises his Dex to 16. They both have the same chance to hit, but Caramon is doing 2 more damage. On the other hand, Tanis can use a bow much better than Caramon, and he gets the other benefits of superior Dexterity as well.
I guess that addresses one aspect of the problem.
Maybe something like letting certain characters or certain sorts of spells or weapons use two stats instead of one? Such as combining STR + DEX for attack rolls (to a maximum of +5), so you'd want a 14 and a 16, and you'd be good? Of course you could /start/ with a 14 & 16, but not a 20, so it'd have to be level-delayed for the sake of balance...
Or something similar in stat-pairs for saves?
I don't know, if it were easy, they'd've done it by now.