I think the sort of wheely case Robin is describing is quite high-tech, and with adequate and substantial internal padding, and sprung suspension on the wheels, it would probably be OK, although expensive and heavy in its own right.
However, I've quite often seen people using wheeled frames like shopping trolleys (but with the shopping bag removed) with the instrument in its standard hard case strapped to the wheely frame with bungey cords or straps. Typically they have no proper padding or suspension and often used by morris musicians at festivals lugging their boxes from one dance spot to another. Sometimes the wheely frames are also loaded up with sticks, other bags, beer tankards, etc.
It may be OK if the road or pavement surfaces are nice and smooth but often they are not, and I've seen instruments on these wheely frames being bumped up and down kerbs, and worst of all, being rattled machine-gun like over cobbles and setts, like Whitby's east side streets
. It goes through me to think of those poor reed plates and wax being subjected to such intense vibration
. In this sort of situation, if you don't want to lug a hard case around by hand, I think it is much better for the instrument to be carried in a ruck-sack style gig bag.