Maybe FR only allow a limited number of ID types because it'd become too confusing otherwise for the check-in agent.
In the US I think the rule is 'government-issued photo ID' so military/police etc. IDs would be acceptable.
I wonder if their own staff IDs are accepted? (Note I didn't say 'acceptable').
As for the driver's licence allowed on domestic flights - as there is no further limitation, one assumes a photo driver's licence in, say, Arabic or Korean would be acceptable? Does the check-in agent actually have to be able to read and understand the name?
Maybe we need to think about what the point of the exercise is and make appropriate rules, appropriately.