I don't think there is anything wrong with that approach. After all, the guard appears to have the instructions, "Let anyone in who is a noble.", and this doesn't need to be a situation that requires a lot of time to be spent on it. It's not an exciting moment, so handwaving past it is fine.This is an excellent point, I too would like to delve deeper into social challenges vs. physical ones.
For example: In a recent game, the party had to get into the High Quarter of the city - populated near exclusively by nobles. It's walled and the guards are disinclined to let "rabble" in.
One of the characters was of noble background. He just prominently displayed his family crest and the group strolled right in.
I also don't think there is anything wrong with alternative approaches. For example...
1) How prominent is the family crest in the community? Is it one that would be immediately recognized? I might require the guard to make an intelligence or skill check of the appropriate sort to recognize the device. If not, then the guard might stop the PC and ask for further proof, such a identification papers of some sort or perhaps a check with his superior to see if the superior has heard of this family.
2) How likely is the guard to be suspicious in this circumstances? Are false nobles a common problem? Is the PC's family respectable and universally liked, or do they have a reputation. Does the PC and his 'servants' appear to be reputable folks by the standards of the community, or do they look like a heavily armed band of ruffians and sellswords? If the guard is suspicious or just takes a dislike to the PC (hello reaction check!), he may give the PC some difficulty even if he believes the PC is a noble - insisting on papers, being disagreeable, and making passive aggressive comments.
3) How much noble bearing does the character really have? It's not an automatic that just because the character has a noble background, that he paid attention to his dancing master and has good posture, good diction, and a proper noble bearing. A low charisma noble might be assumed to in fact not have paid particular attention to these fine points, and have wiped his snotty nose on his sleeve, forgot to wash his face this morning, smell of sweaty horseflesh, and generally giving the impression of not being what the guard expects to see in a noble. He might behave like "rabble" no matter how high his lineage, and so provoke suspicion and perhaps dislike from the guard on those grounds. That after all is one reasonable expression of what having low charisma means.
I'd typically allow some chance that the player was refused admittance even though he had every right to be there. Maybe the DC to get past the guard is 0 if you are really a noble, and 20 if you are not. If you have a -8 on your social check, which is not at all impossible in my game, that would still mean you had a 35% chance of having a hassle even if you were a noble. In fact, you might find that the party rogue, with +12 bluff check and appropriate insight that the guard was corrupt and open to a bribe (thus getting a circumstance bonus) actually has a better chance of getting you in that you have.
The other thing that differs in my approach is that "noble background" or anything else in your background that can be a tangible advantage has to be paid for at character generation. There is literally a trait in my game called "Noble Rank" that lets you start the game as a noble, among the many advantages of which is that you are presumed to have reason to move in noble circles, and have a effectively +3 bonus on social checks in any situation where the NPC recognizes and respects your rank. And if you also want to be "wealthy" there is a trait for that. Heck, you can start play as the king's third son if you are willing to pay for all the advantages that you want to start with like wealthy, patron, high noble rank.
Where I've seen your example go wrong is when a player tries to leverage all sorts of advantages out of his background, or particularly out of the absence of his background, by browbeating the DM into accepting that he could in fact have this in his background, and if he did, then he shouldn't have to roll. That can get to be a problem, with people treating color in their background as if it was an advantage on their character sheet. Hence, the reason for assigning typical background claims to mechanical advantages is not only do I not have to say "no" to such things, but if someone tries to leverage their background, I can point out that they didn't pay for the advantage they are trying to have.
Likewise, one potential problem with this approach is that if all the PC did was display a device on his shield or tunic, I can foresee a PC arguing that all he needs to do is by a fake shield and display that without needing a roll and that being an argument.
How exactly I would approach this depends a lot on what I would think is good for the game at the moment. Is it worthwhile to highlight the noble PC's low charisma and the parties mercenary appearance? Or, is it better to just ignore any minor problems and role-play opportunities highlighting that might bring and get to the good stuff? That's a pure judgment call with no right answer.
I can relate that about 1/3rd of the way into my campaign, the PC's moved their base from their home capital city to a foreign capital city, and had to move through customs and get papers, and I made the call to RP that out because it was also an opportunity to info-dump and get important information about the new city (and its laws) into the hands of the players. One of the players had a pet grizzly bear. "No problem." asserts the customs officer. "Plenty of animals in the city. We have a strong elven community. Just don't leave your pets unattended where they might cause a disturbance." (Naturally, one of the first things the PC did was leave the animal unattended.) One of the characters was a hobgoblin. THAT required a bunch of social rolls by a PC in the party with noble rank, including some name dropping, to even get the hobgoblin into the city - despite the fact that the hobgoblin was dressed appropriately for a gentlemen's man-servant (which he in fact was). The refused to even talk to the hobgoblin, and if the hobgoblin had insisted on talking to them, given the xenophobia penalites involved and the hobgoblins lack of social skills it's highly likely they would have imprisoned or killed the hobgoblin on the spot. One of the PC's commented to the hobgoblin, "It appears that they consider you a lower form of life than the bear." Yes, precisely.