There are a very small number of specific events where ruling dynasty does matter. For example if you play Delhi, you start with Sirhind as a vassal, ruled by Lodi dynasty. There is an event that forces you to release them as a vassal or go to war against them, but only if they are ruled by the Lodi dynasty. If you use the subject interaction to force a relative onto their throne, the event will never fire, and you'll avoid a war with them.
Generally it is an overall benefit to have your dynasty on more thrones, and with your own vassals it's sort of a long-term investment with a LD cost for an LD reduction over the long term (assuming you are willing to fight any pretender rebels they get).