But it's possible to resolve all this stuff during the course of play. And possible resolutions aren't hard to think of - anything from the PC has been travelling incognito to the PC has been banished because on the losing side of a power struggle to the PC's family is impoverished and hence the PC went out to try and make his/her fortune.The bigger headache, no matter what the rules are, is if you're declaring you're a noble now that means you've in fact been a noble all along; which in turn means the question of your entourage (what it consists of, its general level of loyalty, its capabilities, and [most important to play!] whether any of it would have come with you into the field) should have been dealt with before you first entered play.
Again we see three things:It's an even bigger issue if you're like me and have nobility actually mean nobility, and not just as some empty title and a PC who wears nice clothes, and is stuck up. If a player is nobility in my game, they have access to tremendous resources and influence compared to other social classes. That sort of advantage is not something that I will just let a player pick at the drop of a hat.
(1) A strong assumption of GM authorship/gating;
(2) Assumptions about the fiction;
(3) Assumptions about system.
(2) Assumptions about the fiction;
(3) Assumptions about system.
It's actually quite easy to have fiction that involves a noble who lacks the sorts of resources and influence you refer to: I mentioned some possibilities earlier in this post, and examples from fiction/legendary history abound: Aragorn; Richard the Lionheart (at various points in his endeavours); some versions of Robin Hood; and the film Hari-Kiri: Death of a Samurai are the ones I think of straight away. There are also strictly historical examples such as White Russians in exile, Free Imperial Knights in the last days of the Holy Roman Empire, and the like.
As far as system is concerned, there are many ways to treat nobility. In Classic Traveller, every PC has a Social Standing score, and a 12+ indicates nobility. In my game, when the players (as their PCs) are debating what course of action to choose, I sometimes call for opposed checks to resolve the dispute, and allocate bonuses for nobility (as well as appropriate skills like Leadership).
In Burning Wheel, characrers who are Born Noble acquire the Mark of Privilege trait, which confers an advantage on Circles checks to meet members of the nobility, but also imposes a penalty on Inconspicuous checks to move among the common folk. Whether a PC who is born noble has many resources, or few, will depend on the choices made by the player during PC building (BW uses a fairly complex lifepath system) - obviously being wealthy has its advantages, but so does being a mage who knows lots of spells, and the PC build system makes it hard to have both.
In Cortex+ Heroic, being a wealth noble could be expressed as a Distinction, or could be the fictional logic behind an appropriate skill - but the dice added to the pool for such abilities are no bigger or greener than the dice other players get to add for their PCs' abilities. HeroQuest revised would treat nobility in a similar way. In other words, it is possible for wealthy noble to be a defining trait of a character without that character therefore dominating play - because in mechanical terms there is no need for that trait to be more significant than any other PCs' defining trait.
Obviousy some systems treat nobility as an aspect of colour/flavour, rather than a discrete system element. Rolemaster is an example: in one RM campaign I ran two of the PCs were nobles (samurai), and this fictional positioniong obviously conferred certain benefits in some social contexts; but the other PCs also had interesting backstories (eg one was formerly an animal lord, who had been banished from Heaven and stripped of powers and memory as retribution for wrongdoing).
The last time I played in an AD&D campaign, my character was a noble (from memory, I had taken the Cavalier kit from some rulebook or other). It had relatively little impact on play. My backstory explained why I didn't have an entourage.
The idea that having PCs be nobles will break the game in some way, and thus needs super-special GM policing, isn't something that I've seen in my play experience.