It doesn’t work that way.
To claim a Noble Title, you have to have a casus belli (or CB) and perform a Coup. There are three ways you can go about getting a CB: Favor, Fame, and Wealth. Note: the last two only apply to non-Nobles. Once you become a noble, only favor can be used.
Favor: Let's say I'm a Mayor of a city in some county. If I can gain enough “favor”, I can either take over as Count of the county, or if I have enough land can claim independence and create my own county. What does “favor” mean? Favor is a willingness by your peers, your noble's peers, or your noble's liege lord to support you. This is actually a written contract that they sign that assures you their support. So if you're a mayor, and you can rally enough other mayors (currently 2/3), you can claim CB and attempt to overthrow your count. As previously stated, instead of getting the favor from the other mayors, you can alternatively curry favor with the other counts in your duchy - your count's peers. If you can get 51% of your count's peers to agree, then you have achieved CB. As with before, that gives you the opportunity to perform a coup. Finally, if you can get 25% of your count's peers and their duke you’ve established a cause for war. For King, there are no nobles above them. So you either need the dukes to rally against the king, or you need to gain favor with the other Kings.
Fame: Each noble title has its own fame. Legendary for Kings, Exalted for Dukes, and Renowned for Counts. If you can reach the level of fame just below a noble title: Famous for Counts, Renowned for Dukes, and Exalted for Kings, you can automatically claim CB on the basis of being famous. Then, the same process repeats as before. Of course, being an Exalted character might give you CB to claim the title of King, but you still need an army to defend your new capital. That's where more politics are involved. And as an Exalted character if you die while challenging the King, you suffer the spirit loss of being a now, Legendary character.
Wealth: If you're able to accumulate some, yet to be defined amount of wealth based on play-testing, you can buy a CB. Of course, you still need the land to claim as your own, and you still need to pay mercenaries in order to invade/defend your new title, but it’s at least possible to get the CB.
Just because my pappy was a king doesn’t mean I have a claim. I may have more wealth and fame to start with but I don’t have an automatic CB nor does the rest of my family. Only the previous holder would have a chance to retake the title.