Is there a way to remove the AI option in the Adobe Stock search so that it stays off at a usser account level rather than having to remember to switch it off for each search?
No, the search options are not "sticky"; you have to set them for each session. This would be a worthwhile feature for Adobe to add, so perhaps you can submit it as a feature request.
It would be really helpful if there was an option to exclude or include Adobe Stock AI images at a user account level rather than having to remember to switch it off for each individual search.