It's not something I've ever personally done before, but I like the idea! I think it also begs the question of what exactly would the most story-relevant parties be for some games?
For example, in Suikoden IV, even if the 'original gang' is Chiepoo and the Razril Knights, I think a party of Lazlo, Lino, Kika, and Snowe makes the most storyline sense as those are the army's most important leaders. You could then send the Razril Knights after Cray as a consolation prize.
For Suikoden II, it's tough since Nanami isn't available. I'd say Riou, Viktor, and Flik are necessities, then maybe you can fill it out with Chaco, Sierra, and Shin who show varying levels of relevance throughout the game? But it's up for debate, I guess.
And just an extension of these thoughts, but I would love for people to come up with storyline-relevant parties for multi-party scenarios, like the Night Raid in SII or the Ashtwal Mountains in SV! Would be interesting to see what people come up with.