There are things that we do not know and these might impact our answers. But based on what we know so far this is my best guess at the explanation. You do tell us that the default route learned via area 1 is external. You tell us the ASA also learns a default route via area 0. I am guessing that this default route from area 0 is an internal route. OSPF will always prefer an internal route over an external route.
I finally found the issue. The edge router was configured as ospf point to mulitpoint. ASA does not support that type of network. Changing the network to broadcast type on the Edge router enabled router to be injected.
Thanks for the update letting us know that you have solved your own problem. And thanks for telling us what the problem was. I believe that this might be helpful to other participants in the community.