I've talked a little bit about the feudal system elsewhere, and in your question I see a lot of fallacies that are the result of a broad education in Medieval Europe, because honestly no one needs a specialized understanding of the "Feudal System" unless they're writing a book length work about it or are teaching grad students. So, if you don't mind, I'm going to use your question as an excuse to teach a little bit of a feudalism class which should have the convenient side-effect of answering your question.

A quick aside, I will be moving forward assuming you've read the other answer because we've got a lot of ground to cover.

When someone takes a class like MED3030 or something similar they are taught about two political and economic systems that were extant during the Medieval Period, these being Feudalism and Manorialism. Feudalism is described as a complex web of oaths, loyalties, and responsibilities between a king and his vassals and those vassals with their own vassals. Manorialism is described as a system of lords and tenant farmers who have mutual obligations to one another. The feudal idea is then related to the Roman patron-client relationship and the manorial idea is related to the Roman latifundia. However, should we look closely, all that's really being described here is a chain of authority rather than a system of government, and trust me on this, a chain of authority does not a government make.

The second thing that people are usually taught is that while the king was a King, he usually didn't have much control over his vassals, because said vassals could run around with their own private armies and cause all sorts of mischief, such as not bringing their private armies around when the king calls for them. This fallacy is a unique combination of the danger behind generalizations and the actual history of Medieval Europe. Specifically, the cases of the Kingdom of France and the Holy Roman Empire (starting with Otto I, not Charlemagne). The Holy Roman Empire had the misfortune of being an extraordinarily powerful state at its birth (962 AD), so much so that for nearly a century the Emperor in the West had the Catholic Church (here used to refer to the Western Church, there was no such thing as Catholicism yet) under his thumb. While this state did indeed suffer many civil wars, the Emperor maintained firm control over his vassals and his Empire. The dukes were kept in check by both law and theology, and the Emperor maintained his royal rights. Up until the Investiture Controversy anyway, after which point various Emperors sold the rights of the office in return for the office it self, creating an empty title which ruled over hundreds of functionally independent states (~1250). So from 962-1250(ish) we see a strong centralized monarchy that slowly becomes the Holy Roman Empire that we all know and love.

At the same time, a little bit to the left, we have the Kingdom of France. Which was going through a low period at the same time that the HRE (Holy Roman Empire) was reaching its height. The Karolingian kings had very little actual power within France, and the Capetian kings that followed them were much the same, to draw a convenient (if inaccurate) comparison, France moved in reverse relative to its Germanic neighbor. The Capetian kings were so weak that they could not reliably control the lowest Count in the Ille De France, let alone the great dukes of Aquitaine or Toulouse, but ever so slowly they gained more and more strength and control (this is over the course of about two centuries), such that when the HRE was sliding toward decentralization the French Monarchs were approaching the height of their power (again, sorta, but it sounds good in a narrative).

Now here comes the fun part, rather than teach many classes on both the HRE and France, we as educators and historians have decided that if you squint really hard and turn your head sideways you can say that, "generally the feudal monarchies were a collection of powerful vassals with weak kings held together by a chivalric system of oaths and Christianity." (Hell, I'm doing it right now, there's just so much ground to cover) Which leads, ultimately, to this idea of hereditary succession within a Duchy (Hah! I told you I'd get to the question!).

In my other answer I briefly discussed the idea of private property, which is something of a disputed topic among medieval historians, because we are pretty sure that private property as we know it didn't exist during the medieval period, but we are sure that there was property and that it was private. We've gotten around this little issue by calling such property heritable and other property (the stuff the king technically owned) allodial.

There comes a critical point in the lifetime of a monarchy when governors start being dukes. This point is where the heritable property of the governors reaches a critical mass and the authority of the Crown dips below a certain point, it is at this point that the royal right to appointment instead becomes the royal right to confirmation, and (in the case of the HRE) that right goes away (de facto) altogether. This is when, for example, the son of the last duke inherits the duchy, which means that the king is almost entirely out of the picture. Even as I write this I'm tempted to say that this was generally the case, but it wasn't. The medieval period spanned nearly 700 years, and while each kingdom to some extent relied on the old Roman way of doing things they all had their own idiosyncrasies that make it nearly impossible to make any sort of general statement. The true problem with medieval history is that each state is united just enough by their common religious and legal heritage that generalizations can be made, which makes it difficult to not make generalizations.

So with that in mind, I'm not going to try to answer your question in the context of all of Europe over nearly 700 years but instead within a time period and place that I know very well, the Ottonian-Salian period in the HRE (962-1056). Your question seems to be one of private property and inheritance under the feudal idea. This was all relative really, there are some cultural norms of inheritance i.e. Germanic (or Partable) Inheritance where a father would split all of his heritable property equally between his sons, a notable example of this would be Louis the Pious and his four sons. But this wasn't legally so much as culturally enforced. But as time moved on the idea of Primogeniture (Firstborn) Inheritance became more and more common, with one son (not necessarily the firstborn) inheriting all of the heritable property and the other sons being sent off to the church or into some military service. So, they were nobodies, but they were usually wealthy nobodies, and if a Crusade was going on they'd usually ride along with it to make a play for land and glory elsewhere. In addition, a family's land was not necessarily confined to the boundaries of the Duchy that they ruled, we have records of Dukes holding lands all across the Empire, it is only after Dukes start waging war on one another that we see their property coalesce entirely within their duchies. A family could have as much land as they could gain and hold on to really, there weren't legal constraints on land holding (for nobility) at this point in time, for example a guy by the name of Count Guntram "the Wealthy" held over 400 individual (heritable) pieces of property across the Kingdom of East Francia (the predecessor to the HRE). We know this because Otto I revoked all of this land from Guntram because of his traitorous actions and gave it out to a ton of other people all across the Kingdom.

Ultimately you're probably having a hard time understanding what is going on because the period itself is so massively broad and deep and has been presented to you in a completely wrong (if digestible) manner. This coupled with the fact that a lot of things that we historians present as laws, or some sort of rationalized system, is our way of rationalizing a ton of customs into a system that we can explain outside of a master's thesis has lead to much misinformation and unnecessary confusion.

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Sources and additional reading:

Bachrach, David. "Exercise of royal power in early medieval Europe: the case of Otto the Great 936–73." Early Medieval Europe 17, no. 4 (2009): 389-419.

Canning, Joseph. A history of medieval political thought: 300–1450. Routledge, 2002.

De Corvey, Widukind. The Deeds of the Saxons. Translated by David Bachrach and Bernard Bachrach. Catholic University of America Press, 2014.

Fichtenau, Heinrich. The Carolingian Empire. University of Toronto Press, 1978.

Luscombe, David, and Riley-Smith Johnathan. eds. The new Cambridge medieval history volume four. Cambridge University Press, 2004

Reuter, Timothy. Germany in the early Middle Ages c. 800-1056. Routledge, 2014.