Yes, this action is not allowed on a Read Only table. As a rule AppSheet doesn’t allow any actions that add rows or perform updates on Read Only tables.
BUT, The “Add a Row to Another Table” Action is operating on a different table and not impacting the Read Only table itself. I can’t think of a reason why it shouldn’t be allowed.
I would consider updating this post to a Bug, though some might consider it a Feature Request.
In the meantime, I think you can work around this problem by placing an Action on the Read Only table that navigates to the entry form of the table you want to add the row to using the LINKTOFORM function. You can pass the data from the read only table to the form. See pic below.
Not ideal if you are wanting a one-click feature. Silver lining - a user verifies the data and can back out if not the row intended and/or can tweak data before the save.