Less so when they revolt and gain independence. Even further less so when you die and they gain a claim on your empire, push it, and conquer everything that you once were.
I actually prefer giving them independence, whether by gavelkind or grant. If you fear them claiming your Empire, breeding kin who are too far down the line of succession to even get a weak claim is pretty easy, while for the most part you don't have to worry about a younger Empire led by a ruler of the same dynasty as you, especially if you join their wars and very easily get to 100 opinion. Having dynasty members of yours breakaway to found their own Empires in other lands is not only a legit strategy, it's bloody fun as all hell and very helpful to you.
*As mentioned before, breakaway dynasties can adopt the local culture and religion, allowing them to expand into new culture groups without antagonizing the local nobility and peasantry at all.
*They provide a useful buffer zone against enemy powers, as forming non-aggression pacts and alliances with them is very easy to do.
*They can often help establish your dynasty, culture and religion in an area where you might want to take it at some future date, getting claimants from them is pretty easy most of the time.
*Once you're done securing all of your borders with friendly dynastic border states, you can let them spend their money and heirs on wars while you econ and tech up, building out all your realms and maxing legalism/majesty.
But by far the biggest benefit is house prestige. For every title every member of your house has held, the house prestige increases. Subsequently every child born of that dynasty inherits some of that prestige. Yet in player hands, the player tends to desire greater personal power and central control over the dynasty, with as few successions as possible. Yet with multiple counties, duchies, kingdoms and empires all with their own multiple successions - the prestige of the house blows up immensely. The increased prestige subsequently makes all members of your family immensely desirable in marriages for prestige purposes, as well as in selections for holy orders and religious head elections. This can eventually reach a tipping point where the innumerable AI dynastic lines of your house begin taking over everything, because no one wants to stop marrying them, no one wants to stop electing them, and there are far too many to kill them all.
This increases your score and if you ever want to unite the family into one world monarchy, as opposed to several disparate ones, you need only collect claimants or use ultimogeniture.
Alternative scenario- they remain your vassal, but support in a revolt a claimant not of your dynasty's claim to the throne (why the AI would act against their interests, I do not know, but I've seen it enough to know that they do). Same outcome, effectively.
Usually when the AI does this, it's because they owed a favour to the claimant and got pulled into the faction unwillingly, or got pulled in through some intrigue. And while this is a terrible situation, it's not one unique to the strat, and can happen with all strategies. It is also mitigated with the elimination of such claimants (whether by assassination or imprisonment, or the deliberate triggering of a rebellion when you have your mercs/guard sitting on their capital), to such an extent that you have all outcomes secured (within a reasonable extent. Sometimes bad luck simply happens). But if you get to the point where other members of your line are spreading their Empires throughout the world, there is nothing to fear, even if you end up as an exiled Icelanding count, your house prestige will continue accruing you more score while you reconsolidate the family on the ground level.