Years ago that was the case. You usually wouldn't of even had a composite input on a smaller set (Such as a 13" tv) during the 1990's.
But during the last few years of CRT production, premium features trickled down to even small budget sets. I have several cheap late model CRT's in the 13" range that offer stereo sound, secondary side or rear composite inputs to easily swap things out, flat screens, and s-video and component connections. The type of set you could buy for under $100 at a Wal-Mart before they started to disappear a couple of years ago.