I did move half a year ago and had just to bring my card at the town-hall,
it took exactly 30 seconds (excluding waiting my turn) to change the addr of my card.

So it is changeable !

Btw, there are even empty slots for extra keys (gpg/cacert/...)

No, there is no need to distribute your public key separately as it is distributed with your signature. The only thing the other side needs is the public root-cert from Belgium.

But YES there are some (other) security design flaws in the system of the card. But that wasn't the main purpose of my reply