Why take full backups when you can do COPY_ONLY?
As long as you don't care that:


in the async model, the REDO queue may fall way behind, so the backups on your secondary may not represent the point in time that you think they would if they were taken on the primary.
you will not be able to use DIFFERENTIAL backups in this model.
in the event of a restore, you will have to manually determine which log backups contain the LSN ranges you'll need to restore on top of the chosen COPY_ONLY backup and, given the above, the timestamps on the bak/trn files may not be accurate enough to determine the set of files and sequence you need.
backup history will not be recorded centrally.


Also, I still think there are going to be scenarios where this ultra-long log chain, or relying on a COPY_ONLY backup taken in between log backups, are going to make it difficult to restore. Personally, I would be keen to perform a full, proper backup on the primary on some regular interval, say once a week. YMMV.