Even with expertise a flat +2, the will be likely as good or better than the non-rogues at things that are important to them. Our current +2 to +4 expertise rule works okay, I was thinking more of a flat bonus to keep it simple. I toyed with half proficiency but if I boost proficiency to +11, then expertise would max at +5... I am not sure about that.
They won't, though. Suppose you want to build a lightfoot halfling rogue that specializes in talking and noticing things (in particular, focusing on Persuasion, Deception, Insight, and Perception), but also wants to be capable in combat. They've got to invest in DEX and CON to survive and do damage, and they want some WIS and CHA to support their skills. So maybe their starting array after racial bonuses is 9,16,14,8,14,14. Then there's a sorcerer in the party, with persuasion and deception, and a cleric with perception and insight. All of them bump their main stat at levels 4 and 8, so now the sorcerer has 20 CHA and the cleric has 20 WIS.
With a flat +2 for expertise, the rogue is always going to be slightly behind the sorcerer at talking, and slightly behind the cleric at noticing, unless they put ASIs into CHA and WIS (and how often have you seen a character put ASIs into abilities that have no impact on their combat ability?). And that's with a pretty hefty investment into those ability scores on the rogue's part! A more typical case would be having 10s or 12s in tertiary stats. Yes, neither one of those will be as good at all four at the same time as the rogue, but it would be kind of deflating to pick a skill monkey class and not be the best in the party at the skills you choose to specialize in.
The other reason I don't like a flat bonus is that it means that the distinction between non-proficiency and proficiency becomes more meaningful as you level, but the distinction between proficiency and expertise becomes relatively less meaningful. It seems weird to me to say that getting more experience doing the thing you are considered an "expert" in doesn't let you further distinguish yourself from those who are merely trained in that thing.