But that's what Im trying to point out. At level 1, it is supposes to be a small difference. Even at level 4 it is meant to be small. As you get to higher levels the gap increases. A level 8 Rogue will have considerable advantage over a level 8 fighter at Lock Pick, Stealth, etc. However, at level 4 it is not as big an advantage.
If you increase the prof bonuses at level 1, you will severely skew the bonuses at later levels.
This is something I don't understand (and I'd like to)
Do you have exemples with numbers and/or situations in D&D rather than a comparison with school ?
The differences between characters that use skills they're proficient with is still the same even if everyone have a +2 bonus to anything, right ?
Just forget that OP call this "proficiency bonus".
I.E the level 8 fighter will still roll with the +2 bonus suggested by 1varangian because he's not proficient while your rogue will with +5.
EDIT : writing what's in the spoiler I realize that maybe I missunderstood what OP was asking for.