Well, not maybe 24/7, but rather 24/5. Here in the Boston area, we got our first 24 hour station when WCVB-TV began "5 Avell Night" in the fall of 1972. Part of the reason for WCVB-TV to go 24 hours was in their original license grant after beating WHDH-TV for the Channel 5 license on 3/19/72, to provide the largest amount of local programming possible. This was the first step in that station's quest for excellence (which they did quite well!).
In New York, WCBS-TV (Channel 2) and WNEW-TV (Channel 5) were running all night movies in the early 1970's. However, only WCBS-TV continued with all night programming through the late 1970's. Eventually, all major Boston and NYC stations went 24/7 by the mid 80's.
Funny thing about WCBS-TV (Channel 2)..... they would go through a complete sign-off including "Give Us This Day" at 5:45 AM. Then... they would go to the WCBS-TV "bullseye" test-pattern. And then...... they would sign-on at 5:56 AM, with another episode of "Give Us This Day" followed by "Sunrise Semester". Figure that out! We had WCBS-TV available overnights here in Massachusetts on cable.