They did. On the movies themselves. That jingle was for promo ads.
The lyrics for The Late Show (movie) opening theme in the 60s and 70s on CBS O&O stations:
The Late Show,
Relax, enjoy a snack, and watch the Late Show,
Channel (insert number here) is proud to bring the greatest of stars
Here on the great Late Show.
I thought they used "The Syncopated Clock theme".
No, that jingle was the opening theme
for The Late Show - at least in LA on KNXT. I was thinking as early as the late 60s. but I'm sure it ws used in the early 70s, and up until CBS first started to supply network programming at 11:30. I know that when Merv Griffin was on CBS,, The Late Show
movie was pushed back to 12:30 or 1:00 AM, and again, they used that "jingle."
Most people will recognize the Syncopated Clock -
music - it was used for many things over the years. It was probably used as the Late Show theme up until the time of the "jingle."
Strange . . . in New York on WCBS-TV, the jingle was for promos, and the "Syncopated Clock" music was used for the opening. In fact, both films are on this link:http://www.tvpmm.com/documents/364.html
(note that the picture is a bit ahead of the sound in terms of sync in the "Syncopated Clock" open)
This jingle may well have dated to 1965 - the year the CBS O&O's started airing films in color. (The funny thing was, at least WCBS and KNXT, possibly Chicago's WBBM, used the same (eye)2 logo, with the 2 set in Grotesque No. 9, during the '60's.) I've heard that WBBM likewise used the "Syncopated Clock" open as on that link. (As 'radioman148' duly noted.)