I don't think this is really true due to the disparity in the races, classes and subclasses.
At most levels a Dwarf, Goblin or Shadar Kai Wizard with poor ability rolls (say 22 point buy equivalent) is going to be higher powered than a Halfling Monk or Barbarian who rolled very, very well (say 35 point buy equivalent).
I guess I will just disagree with this. The most common check I see in campaigns that are even combat focused are skill checks, which use a variety of abilities. Being just better overall at that means you are just better. And for most characters, building around a particular ability score is part of playing the character. In the game I'm playing in right now, I am playing a bard. My goal for that character is to get Charisma as high as possible because just about everything I do is based on that ability. My next character is a bladesinger. Again, Int is the focus for the character.
Being able to reach the stat cap with only one ASI is immensely powerful. It frees me up to do much more interesting things with feats for the character. The difference between, say, a 16 and an 18 is huge. Now imagine multiple 18s. A character with low ability scores it looking at spending the entire game catching up with another character who will just be better.
Now yes, there are some classes that are just not as good as others. That, however, isn't something for ability scores to fix. That's for the designers.
I get that not everyone feels this way, and I'm not going to tell anyone they're wrong. It's just a no-fly for me personally. The notion that it makes me somehow a power gamer is just silly. I'm not interested in being the star of the show, and I want everyone to shine, it's just that simple. And as someone who GMs a lot, a character who's just not as good as the other characters mechanically isn't something that I view as being made up with roleplay, or class selection either. It's a YMMV situation, and definitely yours does.