What you’re talking about is just a "7 inch SINGLE invented by RCA long before the first "12 inch single appeared on the market.
Every radiostation played singles (one song per side) back then, also every club deejay played singles. This is professional format to promote hits, but please keep in mind that many small independent record labels never released any LPs (just 45s), some of them are private press. It was just a handy format to sell music. Special Promo Singles also pressed prior to LPs (if they were any) to promote new music.
In Jamaica they pressed only "7 inch singles (45s) for example.
Jukebox is just a player in public places for already well known music.
But to make a hit they need a radio dj and promo 45s (singles) to break the record before it became a hit. Same about local discoteques back in the days (in the 70’s).
Music released on "7 inch single is often different version, different take of what they released later on LPs.
Later when "12 inch 45rpm single was invented that was extended version of the song, often different take, sometimes absolutelty unique version available only on single and not available on LP. There was a maxi single format as well with many different versions of the same tune.
This is a whole different culture, compared to what a typical modern audiophile pressing company is doing now. What they do is just a regular LP (originally pressed on 33rpm), but re-issued on 2 x 45rpm "12inch LPs for better quality. Sometimes re-mastered in half speed. But it’s the same music as on the regular LP.
The culture behind the "7 inch 45s and "12 inch 45rpm singles (or maxi singles) is a whole different story. This is not about speed or size, it’s about different version, extended version, different take or remix. This is what makes those records unique, not just different speed or rotation on turntable.