My Monday night yoga teacher had us do the Pigeon last class. Was I ever surprised to discover that with flowing movement (Vinyasa-breath synchronized movement), I found my hips just sinking down. Not everyone is going to have that experience their first try (I'm fairly flexible to begin with) at doing a full Pigeon pose but I think everyone will find their hips opening up with the help of careful instruction and Vinyasa over time.
When I first started doing yoga, I did not understand why "Downward Dog" was considered to be a restful pose. My feet didn't touch the floor, as the teachers' did and that certainly wasn't restful! However, over time, my feet touched the floor. My hamstrings are open. Sometimes I use my flexibility to balance myself, as I can often lower my heel to the floor without coming out of a pose.
I'm glad you find downdog to be restful but I never have after doing it for many years. And I still can't put my heels on the floor...genetically tight hamstrings, what can I say. Never mind my naturally hyperextended arms. So more power to you...personally, I find downdog to be one of the most strenuous and annoying poses ever created. I find tree pose more restful! :-)