I disagree, there. Not all peace should be diverted via the liege - not least since that'll severely cripple the efforts of anyone attacking any significantly sized kingdom.
I agree with mobilisation = DoW between that vassal and your enemies, but fragmented peace should still exist - not least because it did. In the HYW, England wasn't at war with all of France all of the time, nor was it required to crush the army in Paris in order to expand their holdings in Gascony. The logic of that is tenuous at best.
Say that I'm the Duke of Catalonia, pursuing a border dispute against the Duchy of Toulouse, or someone similar. My DoW on him naturally brings the King of France to his aid, and that will bring the King of Aragon to mine. From this point forwards, I have no diplomatic actions available to me except for wiping out the entire French army and hoping my liege makes an acceptable peace on my behalf. That makes that kind of border dispute virtually pointless to engage in unless you're on the Kingdom tier, or are a very, very strong independent Duchy.
Currently, I have the ability to strike Toulouse swiftly, before the French King can respond. I still have to hold him off, or make some kind of peace settlement with him personally in order to save my own lands, which as anyone who has been in similar situations will know is incredibly unlikely without having beaten him conclusively on the battlefield.
If he has no claim on me then I assume you could argue that my swift border move is almost an exploit, given that the French King, even if victorious, cannot require me to give back the land. If that's the logic, then it'd be far easier and better gameplay wise to give the liege a claim on anything which a vassal is forced to surrender.
That way, the Duke of Toulouse would get a claim against me for any of his vassal counts that I depose. Ideally, you'd also pass on those claims to the King, so that for every piece of his kingdom I chip away, he has a legitimate claim to pursue against me in his inevitable counter-attack.
That seems better, IMO, than refusing diplomatic ability to anyone who is not top dog in the pile.