They are supposed to be a way to convert territory into fleet power without increasing your admin. Vassals are supposed to send their fleet to join yours in war.
You can use vassals as buffer states between your own Empire and enemies, so that when the enemy declares war your vassals get ravaged instead of you.
These factors alone can make vassals worthwhile.
It can also be a relatively quick way to gain control over large swathes of territory which can later be integrated for direct control, only without the unrest etc of direct conquest.
It's still very situationally dependent, and I haven't played vassal heavy in the current patch, but I think the removal of the domination tree requirement for vassals is a huge improvement. In my opinion this requirement had completely gimped vassals for a while, as the tree was completely useless for anything other than vassal heavy play, I
always left it till last and only really wanted the AP from completion. By that time I had completely bypassed the entire phase of the game where vassals were actually useful.
The new megacorps empire type has access to a new subsidiary vassal which is definitely beneficial to them. 25% tax on their energy income and opens their planets to establish branch offices. With the steeper penalty a megacorp faces for going over admin cap the use of subsidiaries seems like it might be invaluable for dominating the galaxy.
Edit: forgot to mention the humble tributary can be excellent for boosting your economy at the expense of someone you don't want to conquer just yet. It will help keep them weak and you strong until you do want to finish them.