"But how can you justify a player character with a (non-disinherited) noble background in a dungeon-crawling fantasy game" well, the most obvious approach is a fantasy setting whose nobility practices cognatic primogeniture where, instead of "first son inherits, second son goes into the military, third son becomes a priest", it's "first son inherits, second son goes into the military, third son becomes an adventurer". From the player's perspective, it handily explains why the title comes with little material support from the family; from the family's perspective, there's an unspoken understanding that most of the spare heirs will be eaten by a dragon (or whatever), thereby simplifying the inheritance situation, and the few survivors will become great assets.
(There is, of course, the possibility that a surviving third son, having grown powerful and understandably harbouring some slight resentment, may return, kill his elder brothers with dark magic, and take over the dynasty, but in practice this almost never happens.)
