I couldn't disagree more. Backgrounds are what you were born, Classes are about what you do. There is no inherent reason why a noble should or shouldn't be a fighter or a wizard - or the balance between physical skill and magic. For that matter there is absolutely a case for a warlock noble, either getting their powers from their hereditary pact or from their land or people.
I didn't say a noble can't be a fighter or wizard. I'm saying I would like the option of an adventurer who leveraged his wealth or was forced by his title for special training
And what disadvantages? But seriously I think you're looking in the warlord or marshal category.
The 4e warlord is far more flexible than that and goes right down to the lazy warlord that never makes an attack in combat. I think all the PHB options were frontline - but the later options increased the flexibility.
A warlord or marshal would just be one option. But It's not the only option as different cultures prize different things in their nobles. And many cultures have elite schools for their nobles with different training programs than the commoner ones.
Other than e.g. ritual casting, some multiclassing, and some other stuff. Or if you want a low-medium magic spin there's the bard which needn't be that magical. This also is why the noble as a class is a bad idea - nobles can be very different.
That's the thing. Nobles can be different.
3e multiclassing was a mess
4e multiclassing was a chore
5e multiclassing is better but it still leaves gaps.
So I think it would be better to have base "face skill expert" noble then offer subclasses to make a heavy warrior noble, a duelist noble, a military officer noble, a criminal noble, a clerical noble, a wizard noble, a dark magic noble. Picking 2 sublclasses as tutors.
The Dragonlance noble would choose a military officer tutor and a bardic tutor
The Warlord noble would choose a military officer tutor and a heavy warrior tutor
The Barbaric Chief's son would choose a barbaric tutor and a shaman tutor
A FR noble might could an exotic weapons tutor and a fencing tutor
A drow noble traitor could choose an assassination tutor and a cleric tutor
A noble form amagocracy might pick a wizard tutor and a sorcrerous tutor.
Another noble might choose a religious tutor and a archery tutor
A dark cult escapee could an assassination tutor and a dark pact tutor
The core D&D classes are too focused on mastery of specific things and none of the multiclass systems work enough to get the right levels of skills and arms without many unwanted aspects.