About 75% of the time I don't get asked for ID at all when flying within Schengen Europe. I understand technically there isn't any border crossing, but they have absolutely no idea who is actually on the plane. Wild.
Asking for an ID or passport when embarking/disembarking would be similar to having an ID check at a border, and would therefore be a border control, i.e. no longer free travel.
Of course Schengen countries have the right to temporarily re-enable border checks.