I hesitate to answer this for two reasons: it may edge pretty close to the "less than 20 years" rule, and it may delve strongly into opinion. I am only one Deaf person; I would encourage you to post in /r/deaf as well to get multiple perspectives.

To keep it factual, I can note that songbooks providing ASL signs became popular in the mid-1990s. Songs in Sign by Collins and Kifer from 1995, Gaia Tossing's Sing'N Sign for Fun from 1996, etc. were picked up by elementary schools and public libraries and contributed to the popularity of hearing children signing along with songs.

The Mormon church also seems to have included ASL in their Children's Songbook in 1989, but that seems to be an isolated publication and not related to its use in public schools and elsewhere.

Speaking as an individual, I appreciate the effort to teach signs, though as you note it isn't really perceived as such by the children or the audience they perform for - it's just play. If a couple of kids actually go on to learn more from it, that's great. If someone encounters a deaf person as an adult and thinks "oh yeah, I remember I learned that song as a kid, I'm not going to freeze up and refuse to try to communicate with this person," that's good too. But I think, for the most part, it's just amusement for the audience and it doesn't have much impact on the deaf community, even locally.

Again, this isn't really an easy question to answer, as it's a recent phenomenon and not really significant to deaf history. It's a thing hearing people think is cool but it doesn't usually stick.