when did it start becomming common to remake songs?

[minor muppetz]

Rubber Duckie and C is for Cookie have both been remade a few times. In addition to the original Rubber Duckie, Little Richard sang a cover of it in the early 1990s, a newly-filmed version featuring kids taking baths while Ernie's recording plays as the soundtrack was filmed in the 1990s, and in 1998, anew version with Ernie was made, using the same audio from the eaarlier version. I think this one still gets shown occassionally, though it seems like Do De Rubber Duck is shown more frequently.

C is for Cookie was remade in 1993, sung by an opera singer (this one was last shown in the 2004 special The Street We Live On), while a remake with Cookie Monster was made in 1998.