You start to find tune medleys in books in the 18th century. By the time Kerr published his "Merry Melodies" (4 volumes, 1870s-1880s) the majority of the tunes are medlified. So the idea predates recording.

There are some hybrid cases. There are many variation sets from the 18th century where the variation is rather circumscribed. This was particularly common for 9/8 jigs; they would often be composed of 4-bar phrases where the second and fourth bars were invariant throughout the set:

AxBy:|
CxDy:|
ExFy:|
GxHy:|
.
.
.

This looks to me like the result of people writing out improvisations.

Incidentally "Chorus Jig" did start out as a jig. It was printed that way until at least the early 19th century. Dunno when it was first made into a reel.

Most cultures outside the British Isles and North America still prefer to use one tune for a dance. I liike it that way - Moldavian Csango dances can go on with the same oscillating circle pattern for 20 minutes with only one tune, typically a 16-bar reel played over and over again with no discernible variation. It sends you into a trance in a way no British Isles folk dance can.