Most Influential American Musician of All Time?

Yes, but that may also be because of more modern technology. Radio was far more common for Muddy Waters (not to mention John Lee Hooker (but I will)) than for Robert Johnson. If that does make him (Muddy or John Lee) more influential, then perhaps we should keep going forward. Jimi Hendrix....Stevie Ray Vaughn...etc.
Recording/playback was not a huge issue when Robert Johnson was in his prime.

At what point do you stop saying who was more popular and who was more influential?? Yes, modern technology will help preserve/promote any artist popularity. Does that mean that the most recent artist is the most influential?

If so, the Brittany Spears and Jessica Simpson may be the most influential American musicians of all time.......:-(

God help us all.........

Tvad, FWIW I think your definition of 'musician' might be a bit narrow, especially in view of how it's defined in my dictionary, i.e. a composer or performer of music and as an alternative a performer esp of instrumental music.

Re Robert Johnson's importance (to me) I'd never heard of him 'til you mentioned him. I though you were referring to a relatively obscure jazz personality from early 1900, James P Johnson who was an African American composer and piano player who developed the Stride style of jazz piano. He also composed hit tunes, waltzes, ballet, opera and symphonic music. He taught Fats Waller and influenced Gershwin, Count Basie, Duke Ellington, Art Tatum and Thelonious Monk, ad infinitum.

LMAO at my own ignorance and willingness to sign on just to be equitable. I'm not into Blue's. I went straight from hillbilly ('folk music' for the elitists and 'blue grass' for the generic non-hillbilly) to classical and jazz. Who is Robert Johnson? :-)

T-Bone Walker was more influential than Muddy Waters. His writing, singing, guitar playing and dancing were a major influence on Muddy, B.B. King and Chuck Berry. Jimi Hendrix wasn't the first to play the guitar behind his head.

That said, my vote goes to Mr. Louis Armstrong. He invented modern popular singing. 2nd place goes to Nat King Cole. Every piano lounge player is channeling Nat. 3rd place - tie between Elvis and Frank S.