In 1935 Big Joe Williams recorded Baby Please Don't Go with the Joe Williams' Washboard Blues Singers that included Dad Tracy on 1 string fiddle and Chasey Kokomo Collins on washboard along with Joe who sang and played guitar.
Since that recording many other artists have recorded versions including Them an Irish rock that had a vocalist by the name of Van Morrison.
AC/DC and Aerosmith both followed the rock version.
Muddy Waters electrified the song but stayed more to the origin of the song.
A blues standard by any means of the word should include this song.

Here Big Joe Williams performs the song live on his 9 string guitar go figure that?
Must have been hard to tune.