Thanks for flagging this, and sorry it cost you time.
Alt text does work, just not through the post-meta tool your agent probably tried. WordPress stores alt under a protected key, so that route was always going to be refused, and the refusal said “Permission denied” without naming the tool that actually does it.
1.7.0 fixes both parts. The refusal now points at Update media (aafm-update-media), which writes alt through its alt parameter. There is also an “Enable all writes” button now, since Update media had to be ticked by hand and was easy to miss.
If it still gives you trouble after updating, tell me which AI client you were using.