The answer to the question that is the title of your post (i.e. why isn't everything scaled by proficiency bonus) is "because 4th edition did it the way you suggest and it was one of the things people complained about that they adjusted for 5th edition".
I guess that's the elephant in the room, yeah.
5e took a lot of thing 4e did very well, but overtly, and kept traces of them that didn't work nearly so well, but were less obvious.
Proficiency is one of them.
And, yes, granting scaling across the board would be obvious, and thus have invited renewed edition warring. But not really that different. The big change from past eds to 4e was not the magnitude of scaling or the blanket nature of it, but the parity. Prior to 4e, saves had scaled at different rates, skills (when they existed) at different rates, and especially, Attack Matrixes/THAC0/BAB at very different rates. 4e equalized all that. A Fighter's sword attack and the wizard's dagger attack scaled at the same basic rate, the fighter no longer had this widening advantage in combat as you leveled.
That's by far the most significant aspect of what 4e did with scaling - and 5e retained it.
But, another thing is that the scaling is pretty limited...
There's an argument to be made that some folks weren't complaining about the idea of advancing all of the skills by the same amount, just the range of advancement made the numbers too big and adjusted the difficulties by what they thought were ridiculous amounts (i.e. 1/2 level is too much, 1/4 level as per 5e would be fine)
And 5e /certainly/ addressed that, really hard, with BA.
So tossing in /just/ the scaling (not the whole proficiency bonus, just the scaling part that kicks in after 1st), with everything would prevent characters from getting relatively /worse/ as they advanced, but wouldn't otherwise have a huge impact.