Springsteen and Clapton on their favorite, heh, band.

Of course The Band influenced many other bands, but they really did nothing to influence the predominant move toward Psychedelia at the time like the Byrds, Jefferson Airplane and Jimi Hendrix of course.
Other bands that were amazing and mostly forgotten may not have impressed their peers, but left a lasting impression on their fans. In that vein, I was just listening to the first Seatrain disc, which is amazing from beginning to end. I'm sure some would have a field day just trying to figure out which artists influenced their music. 

Yeah @roxy54, I think of The Band (and others like them) as the counter-Counter Culture ;-). The movement they were spearheading was definitely swimming against the tide, and was almost on a cult level. Though their albums did actually sell pretty well, the masses were far more into Hendrix, Led Zeppelin, and soon Black Sabbath, ELP and all the other UK Prog bands.

But your inclusion of The Byrds in the Psychedelia movement is a coupla years behind their timeline. In '68 they were actually a big part of the move into Country, their landmark Sweetheart Of The Rodeo album coming out that year. About as far from Psych as one can get! 

The Seatrain album I like most is the second, s/t one. It contains my favorite version of the Lowell George Song "I'm Willin'". Speaking of them, just earlier today I picked up Peter Rowan's album The First Wippoorwill on Sugar Hill (the great Bluegrass label).

I wonder why Clapton never tried to join The Band after Robbie dropped out? It would have been an interesting experiment and might have given the rest of the guys a much higher profile. Maybe he felt they were too far gone or felt that Robbie was the songwriter and the driving force?

@tomcy6: Because at the time of The Last Waltz, the plan was to take some time off, then later regroup to recommence recording. Robertson wanted to get off the record/tour/record/tour merry-go-round, which he thought was an unhealthy lifestyle. In his book Testify, Robertson says for some reason that just never materialized. I don't think it could have, given Levon's feelings toward Robertson.

Also, while in '68 Clapton wanted to be in The Band in the worst way, by November 25th of 1976 he had established his own "brand", and had a healthy career that he liked going.

As for The Band, they brought in Jim Weider on Telecaster guitar to replace Robertson, a better player in my estimation. But Weider isn't a songwriter, and I don't think Clapton's writing would have fit The Band. And then there is the fact that Levon didn't want to be a backing band for a frontman, which would certainly have been the public's perception had Clapton joined.

It was their lack of new material (both Rick Danko and Richard Manuel never again writing as they had for Music From Big Pink and to a lesser extent the brown album) that crippled The Band Mk.2. And then Richard Manuel committed suicide, a fatal blow. One of the best singers in the history of Rock 'n' Roll, impossible to replace.

As either Clapton or Springsteen said in one of the clips I referenced in the op, The Band were "A miracle".

@bdp24

And then Richard Manuel committed suicide, a fatal blow.

I saw them in concert the night before. I had a great time, even without Robertson, they were great.

I was completely shocked to hear that news a day later.