Their is nothing groundbreaking or even unique about their music--even for its time. Acts like CS&N, Neil Young, Jackson Brown, and many California bands were making Eagles-like music years before the Eagles first album. They didn't create any genres, didn't alter the direction of music, and really didn't inspire many bands.
I won't bother discussing the Beatles, but having them in the same zip code as Led Zeppelin or The RS just doesn't make any sense to me. LZ I came out in 1968, which still blows me away when I listen to it. It is so far ahead of its time. The RS weren't always cutting edge, but pretty much every time I listen to Satisfaction or Paint It Black, I'm pretty shocked to think they both came out in the mid 60s. I will get mocked for mentioning U2, but U2 put out at least four hit albums that sounded nothing like their contemporaries or the popular music of their time--that's four more than the Eagles ever put out. Bruce Springsteen and the E Street Band, Metallica, and Nirvana were putting out hit records that imitated no one and really haven't been successfully imitated since.
The Eagles put out a lot of good music and they are talented musicians, but being a great artist is also about creativity and originality and if you don't bring something new to the table, you don't deserve a seat at the table with the best.