No, the right to live and work is not related to Schengen.

Ireland isn't in Schengen, but a French person can move there tomorrow for work or study etc. They have to show a passport at border control, but otherwise face a very similar situation as they would moving to Germany (fill in some papers, get a local tax id etc).

Minor nitpick: you don't need a passport to travel to/from EU countries not in Schengen as an EU national - your national ID will do.

In practise I forget that, as neither of the two countries relevant to me issue(d) national identity cards (UK, Denmark).

"As an EU national, you're entitled to work — for an employer or as a self-employed person — in any EU country without needing a work permit."

ref: https://europa.eu/youreurope/citizens/work/work-abroad/index....

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.

Schengen is more about removing border controls so that EU can be more like USA in this regard. EU is about alignment with each other on common issues and resources like fishing waters, agriculture, trade deals, right etc.

They each have many implementation details, like if you are in EU but not in Schengen you don't have access to certain common databases.

The desire of countries cherrypicking and sovereignty made Europe very complex structure, I can't wait to have Federal Europe with every country in it with a simplified structure. Can be like US, can be like Switzerland or Germany maybe but thise structures over structures is just way too much and its begging for simplification.

Apparently, %36 of Spanish businesses haven't heard of the Schengen area and another %18 have heard of it but don't know what is it: https://europa.eu/eurobarometer/surveys/detail/3177