I've never known of dacron to quit strething completely...but even it it did, it retains a lot of elasticity. Unstring the bow, it retracts and has to settle back in when re-strung. The elasticity contributes to hand shock, and in some cases noise.
Dacron is much less durable, and harder to get a proper nock fit with heavy-weight bows (string is too fat) and/or small arrow nocks. There's also a performance difference--usually not huge, but it's there.
Thanks for the good word Bjorn and DB!
Chad