It often happens in RPGs that some players work details into their background that can give them serious advantages during play. Sometimes this is intentionally done for the gain, in my experience it usually just coincidental to the concept. There are lots of ways to handle this from the system side of things. Right now I just want to focus on a cheap trick I use to make this sort of request work when it would clearly give the PC an advantage over other members of the party.
Here is my general rule of thumb, if a player character's background will give him or her an advantage, then it comes at a serious price or complication that can only be overcome by an amount of effort that is equal to the advantage it itself. So if you want to be the son a prince, fine. But to make things fair for the other players, I am probably going to have it be a situation where rather than serve as an advantage it serves as a disadvantage initially, until the player character has invested a fair amount of effort.
It should always be related to the size of the advantage. If your father is a respected guard in the city watch, that might require helping him recover from a small scandal. Something that takes a single adventure and isn't too big a deal if you blow it off. But if your the son of a king, it is going to take a full campaign to get things to the point where you can step into the court and play politics. If they want to be from a highly regarded noble family, I might expect a series of adventures to resolve whatever complication keeps them from enjoying the prestige.
Typically if a player asks to be from a highly desirable background, I find most of the time it's because they have a specific concept in mind, not because they are trying to gain the upper hand in the party or have free resources. There are always players who will do that sort of thing, but as I've gotten older, I've found the players in my groups tend to increasingly be the types who are more interested in playing developed characters (regardless of rank, status or wealth). So the aim of this is never to punish the player for having a good concept. It is simply to bring an amount of balance to the situation, adding an investment cost that is more palpable than Flaws or Disadvantages for the desired rank.
This has the added value of building in a challenge for that character, which can serve as fuel for adventures and interactions with NPCs. It is very easy to provide hooks for such a character.
Also I am not afraid to reward the player once he or she gets to the end of the tribulation. Belonging to a wealthy or powerful family is going to have its own challenges and dangers. It could signify a shift in the campaign or, if the rest of the party is onto other things, it could be time for the character to retire and enjoy the position life has afforded.