I thought so for a long time and for me it was the only sensible explanation why you need “designated”.
But since 2009 the Wiki says:
“The value designated is not meant to imply that OpenStreetMap access=* permissions have been automatically “designated” only to that transport mode!”
And other uses of designated e.g. hazmat=designated does not imply the permission only:
So in Germany you can only imply the exclusive permission by the default values of foot/cycle/briddle-way)
highway=path + foot=designated → footway → pedestrians only
highway=path + bicycle=designated → cycleway → cyclist only etc.