I recently did something I swore I'd never do, I submitted to vassalization by a neighboring empire who kept declaring war on me for land grabs and could build ships faster than I could possibly keep up with. It was pretty infuriating that as soon as the truce ran out, they'd start up the next war within a month. I grew so tired of this I finally said "screw it" and accepted their offer. However, I sword I would bust out of this eventually.
After I became their vassal, they started picking fights with their other neighbors, who I had pretty decent relations with prior to vassalization. Despite having an overlord, I took great pains to just keep building my fleet and stay out of the fighting. If my overlords wanted to go to war that often, I wasn't going to volunteer to go into battle with people we still had decent reputations with. In fact I would actively watch battles and hope that my overlords' enemies would come in and wreck all their shit so I could break free with my higher fleet strength once the war was over.
My gripe through this whole repeating process was that any time I would finally have the fleet strength to overthrow my overlords, they would declare war on another empire, and thus I would be stuck in a war I didn't want and couldn't exit out of. I think it would make sense for there to be a mechanic where a vassal could still declare war on their overlords, if anything solely for gaining independence, regardless of their overlords' war status. Then once independence was gained, the vassal could exit the war their overlords dragged them into, or negotiate a peace with their overlords' enemies on their own terms.