My guess as to why hand baggage is restricted on RyanAir is not just that they have the problems of space mentioned above. They have a 15kg limit on hold baggage. If you carry 12kgs (if dense weight rather than bulky) then they can put it in the hold and charge you for it. But then, I always have had a dyspeptic view of FR.
The Americans have got into the habit of carrying on everything because of problems on multi-sector flights. Once hub and spoke routes were brought in, the carriers started losing bags and so pax started carrying them on.
Also, if they are taking sectors on different carriers, they do not want to waste time waiting for the first carrier to cough up the bag. If it does not arrive, they would have the problem of registering the loss and catching the next flight.