True that it costs less, but there are a few restrictions (taken from
www.sportpilot.org):
no night flights;
no flights controlled airspace unless you receive training and a logbook endorsement;
no flights outside the U.S. without advance permission from that country(ies)
no sightseeing flights with passengers for charity fund raisers;
no flights above 10,000' MSL;
no flights when the flight or surface visibility is less than 3 statute miles;
no flights unless you can see the surface of the earth for flight reference;
no flights in LSA with a maximum speed in level flight with maximum continuous power (Vh) of greater than 87 knots (100mph), unless you receive training and a logbook endorsement;
no flights if the operating limitations issued with the aircraft do not permit that activity;
no flights contrary to any limitation listed on the pilot's certificate, U.S. driver's license, FAA medical certificate, or logbook endorsement(s);
no flights while carrying a passenger or property for compensation or hire (no commercial operations).
The first two are the ones that get me. I love flying at night and flying into controlled airspace is a necessity. You are certainly right though and I hope it brings in a lot of people who wouldn't think about flying beforehand. I just hope that you can train for a private pilot's license in a sport plane, I don't see why you couldn't.
EDIT: Personally, if I were to purchase a plane right now, it would be a sport plane because of cost and the fun factor of flying little planes.