I think it's about specialization of labor. 5E allows you to optimize, but it is still is generalist-friendly. As you outlined in your earlier post, Eirikrautha, rigid build-time specialization is a requirement for effectiveness only in a system which is built to challenge specialists (target DCs in the low 30s, etc.). 5E made the conscious design choice to make the d20 roll the single biggest factor in almost any contest of skill, and while I have my problems with that idea from the verisimilitude perspective (the best archer in the world isn't all that much better than a mediocre archer, really?) it does accomplish its design objective: you don't have to rigidly optimize your build to be successful as an adventurer.
I feel like "allows optimization, still generalist-friendly" isn't too far off from describing 4e though. Everyone gets a half-level bonus to everything, which means "at-level" challenges hover around the same odds of success. The world is not keyed to specific level, however, so challenges that could not be overcome before (such as bluffing an angel or whatever) become possible, even (potentially) trivial. In fact, as I understand it, 5e's Proficiency bonus essentially acts as a slightly-flatter version of 4e's half-level bonus--it scales up at roughly the right levels for a half-as-fast growth with a slightly higher starting point (+2 instead of +0). Since this only applies to some things, rather than everything, one might even make the argument that 5e isn't quite as "generalist-friendly" as 4e, though the obvious rejoinder there is just that the numbers aren't
supposed to get so high that an untrained rube couldn't at least
possibly succeed. (The actual implementation of that, unfortunately, appears to vary.)
What is there to D&D combat besides hit point damage and recovery, condition imposition, buffing and damage prevention, and movement? Maybe a completely new role could do funky stuff with initiative and/or surprise: the "forward observer" role. But I'm not sure there's enough design space there for it not to really play as just a type of leader/controller hybrid.
In general, I agree that at least the "traditional" areas of combat contribution are covered by the four 4e roles. So I'd argue that instead of trying to tease out a new combat role, the better choice would be to apply the "roles" concept to the other areas of interesting mechanical differentiation: Exploration and Socialization.
Your "forward scout" role would probably fall under Exploration, as would things like trapfinding/lockpicking, endurance/athletics, and knowledgeability. (Call them Scout, Expert, Tough, and Sage, just for grins and giggles.) Then Socialization would be split into the "nice guy"/diplomat, the "liar"/bluffer, the "bad cop"/intimidator, and...I'm not sure, maybe something akin to a "social controller/leader" e.g. the sort of Bard-like "play a song to set the tone" kind of thing (I'm kind of grasping at straws here; super tired, studying for physics exam, etc.) These would, of course, only be really useful if there were substantially more mechanical weight in the Socialization aspect of the game, but still.