Why call it "Yoga Church"?
I may not have fully addressed the "sustainability" argument. Lemme do that quick.
Basically, it tends to take a fair amount of time and energy to deeply engage with another culture. For instance, I've practiced Tibetan Buddhism for 10 years, and while I got a certain flavour of the energy behind the images of Tara and Guru Rinpoche quite quickly, it took years for it to really sink in. We're at a curious point in Western spirituality, where it seems like most of the spirituality isn't actually Western. I think this points to a growing meta-culture of cultural appreciation, and identification on a world/human level before nation/tribe, but there's a fair amount of cultural appropriation going on in the spiritual community.
Many of us are basically halfway between Eastern (by training) and Western (by birth – to grossly divide humanity along one geographical axis), and I think the name "Yoga Church" does a good job of addressing – even bridging – this divide.