For the same reason (ie PHYSICS) that higher frequencies let you use smaller inductors in a SMPS, you also get to use smaller capacitors.
IIRC, most "older" CRT TVs would directly rectify the mains (60Hz or so), to get their B+ voltages (that was for tubes. Perhaps you didn't mean THAT old?)
(I guess you could be talking about different "big capacitors? TVs never had the huge caps that were present in supplies for digital logic (minicomputers and the like.))