Neonchameleon
Legend
The Skill systems of 4e and 5e don't allow it.
Why?
Because the Fighter is made like an uncultured unintelligent weaponmaster and the rogue is a super-sneaky, master acrobat, criminal mastermind.
4e fighter: Athletics, Endurance, Heal, Intimidate, and Streetwise
5e fighter: Acrobatics, Animal Handling, Athletics, History, Insight, Intimidation, Perception, and Survival
And backgrounds only give you 2 skills.
And that is before you realize that fighters are weaponmasters and martial experts above the skill of all warriors. Tossing every "not a wizard" into fighter just dillutes the archetype. Suddenlyevery noble, prince, and scholar can outduel every orc and anti-paladin.
This critique is extremely dubious once you take backgrounds into account if you are in any way praising the 3.5 noble class. This is due to how narrow and rigid the 3.5 skill system is.
The noble class gives you 4+Int trained skills per level out of 33 skills + 3 families of skill of which (importantly for this concept) knowledge is one of the families.
By comparison the 4e fighter was short-changed by giving you 3 skills out of 17 (it should have been 4) - and you can easily get more via multiclass feats. Almost all 5e starting characters have 4 trained skills out, again, of 17.
Essentially by giving you two trained skills in a skill list that's half the size of the 3.5 one, the noble background is giving you close to the equivalent of four in 3.5. And a fighter ceases to be uncultured when the background provides the culturing. Funny how that works...
And yes fighters are expert combatants, as are at least some nobles. Are you saying Jaime Lannister or Richard the Lionheart shouldn't be considered an expert? Or does the one-size-fits-all noble class once more break down this time by crippling what nobles, historical and fictional alike, can be?
Now there is room (as I have said repeatedly) for the warlord or marshall class - indeed that's a glaring gap (with the warlord being the better implementation). And a lot of nobles are going to be warlords if you make it a class. But this doesn't mean that a one-size-fits-all "noble" class works.