It would be great if we had rest exp. by the time servers for ARR went up but it still doesn't cancel the fact of a weeks cap of rested exp.

Also, even if I think it would be great(even awesome at that), it would go against the lore and not make any sense. If you think about it, from the time Dalamud touched down(1.0) and ARR(2.0), when we reappear, if we would have literally rested during that time-gap, we would've been pretty OLD.

In actuality, time stopped for us between the two realms and we don't get any resting bonus until we find a new home and log out for the night.