Here's why I don't think ability scores matter as much as people seem to think.
Say that you're playing the role of a 4th level fighter, with an 18 in Strength. When you swing your longsword, your attack bonus is +6---you'll roll a d20, add it to that +6 , and hope it hits the target AC that the DM has set. Pretty standard stuff.
That means on any given throw of the dice, your 18 in Strength is going to feel like a number between 8 or a 27, or it's going to arbitrarily hit on a roll of 20, or arbitrarily miss on a roll of 1. And get this: all of these results have the same odds. Your chance of rolling a 2 or a 13 or a 6 or a 20 or a 11 are all the same. Sure, over the span of dozens of rolls, your average attack roll will be 16.5...but you don't get to roll dozens of times and take the average. In that moment, on your turn in the initiative order, you get to roll only once, and the odds will always be the same.
Advantage/Disadvantage, the Lucky feat, Inspiration, Halfling Luck, etc., can give you a little more control over this, maybe a free "Mulligan" or a +1d6 or something, but probably not every round of every combat scene unless your DM is very generous.
Speaking of the DM: how high is "enough" anyway? The target AC is set by the DM, and varies by opponent (and opponent equipment, and sometimes other factors). Sometimes your opponent is an AC 8 zombie, other times an AC 13 skeleton, and other times an AC 18 skeleton in scale armor with a shield--often in the same adventure (or combat scene). That's a swing of up to 10 points--more than enough to swamp any advantage you might get from Advantage, heh--and you have no control over it.
Ultimately, the DM and the RNG have more do do with how effective your character is in the moment than your ability bonus does. When you roll that d20, all of that talk about the Law of Averages and probability curves goes out the window. You will always be relying on a single random number to hit a single moving target, and the +3 difference between a 15 Strength and an 18 Strength isn't going to matter most of the time (if it ever does).
My two coppers, anyway.