Y-Foil Frames Rear Suspension? I have a few questions about the Y-Foil frame (beam frame)

Firstly as far as i have seen, there is no rear suspension system, does the fact that there is no seat tube offer suspension and dampening, or is the frame to ridged and strong to do that?

Secondly, i am having trouble understanding where the advantages come from and why it was banned. I understand that while made from carbon fiber and the shape of the tubing would mean it is lightweight and aerodynamic, but ofcourse a frame with a seat tube can also be designed with those 2 aspects. so what advantages does having no seat tube provide?
I can only speak based on what I have read, but my understanding is that A) yes it has a softer ride quality due to the lack of a seat tube, and B) it was banned for the lack of a seat tube. UCI is pretty strict on what they consider legal and what they don't.

In regard to your final question as it applies to road bikes, I would venture to say that the lack of a seat tube as it was designed for the frame in question does not provide any substantial advantages. Otherwise we would have seen more frames of this shape from other manufacturers and more of a push from the industry to legalize the design for UCI racing. There have been similar designs through the years such as the Softride. They also failed, because that frame shape just isn't an awesome design.