I do think the paraphonic envelopes have much to do with the uniqueness of the vintage string machine. And when you use a long release time, something else happens. Even after the release has faded, there's still a ringing of notes, almost like a VCA Level is up a tad. There's the sound, still shimmering softly in the background. It's probably a flaw in the instrument's design that ends up being attractive, like the over-driven oscillators of a Model D.
I think many of us would find it useful if modern polyphonic synthesizers had the ability to emulate the paraphonic effect. It seems to be getting popular again, but it would be nice feature added to a "normal" polyphonic instrument.