A poncho isn't a perfect system for me for a couple of reasons. Firstly, a poncho is redundant with my rain jacket and rain pants, which I'm already bringing for use on the bike. So, the role it fills isn't ideal, even if it is slightly more comfortable at rest, perhaps.
Secondly, if I were to bring a tarp, I'd bring something like an MLD Dog Tarp for the head section of the bivy, which is smaller, lighter, and cheaper than a poncho.
Dale's point was, however, well understood and there didn't need to be a question raised there.