There is really no reason to not treat strength as an skill that can be maxed-out.
Yes, there is.
Strength is an attribute, not a skill. Skills can be learned. Attributes are just "there" as the frame of the character if you want.
That doesn't mean attributes shouldn't be increasable at all, but at a much slower rate.
Yes, you can go to the gym to get stronger.
But how long does that take?
I'm sure most people would be able to learn to shoot a basic pistol well enough (not pro soldier level, I guess, but anyway) in a week of focused training.
Go to the gym for one week though and you won't have achieved much, other than muscle ache, maybe. It's just a more long term investment.
Of course, in theory you could use the exact same system to represent both attributes and skills, just making some more costly to increase, or something along those lines.
But the separation makes things more intuitive.
There is also the problem about attributes like intelligence, willpower, wisdom and whatnot.
Many people would say that intelligence cannot really be increased - only education of some sort can.
Same with skills. It is much faster to learn to shoot a gun or crossbow than a bow, but if you depicted that realistically in games, almost nobody would ever pick up a bow.
It's just a pretty complex field with many valid pro and con arguments, so to get somewhere in a system you just have to simplify
somewhere and make decisions about where your system is going to fall short.