"the Beatles were the first to popularize having the band themselves write the songs"
No they weren't.
"the first to do a theme album"
You mean a concept album? No they weren't.
"the first to wear long hair"
No they weren't... wait, what long hair? Even though the Androgynous image most of us associate with being "long hair" became popular with the heavy metal movement, there were still rock groups before the Beatles' popularity that had long hair, and many at the same time of the Beatles that had longer hair.
"the first to take rock outside of the tight restraints of the blues progression"
No they weren't.
"the first to do backmasking"
Backmasking was in use LONG before the Beatles; they just popularized it.
"the first to do a psychodelic [sic] album"
Actually, they received a lot of heat for Sgt. Pepper's Lonely Hearts Club Band because there already was a psychedelic musical movement in the U.S., and some die-hard fans saw them doing a psychedelic album as kind of selling out. Though it was nonetheless an extremely influential album.
"What has Tool done that can compete with those credentials?"
How can you expect a progressive rock group to gain as much popularity with general audiences as a pop rock group? Also, Tool wasn't around at the time of the Beatles, so there's no reason to say, "Well, they weren't the first ones to do this!" if one came decades before the other. I personally agree that there can't be one band that's considered the "greatest", since music is an art, but I just wanted to correct a few things.
