Iceland already has freedom of movement (to live and work) due to its EEA membership; and it is only somewhat to do with Schengen, which is about passport free

Iceland already has freedom of movement (to live and work) due to its EEA membership; and it is only somewhat to do with Schengen, which is about passport free travel not living and working. You can have FoM without Schengen - e.g Romania until 1st Jan 2025.