Defining “the Greatest” is pretty darn hard.
However, my WWII veteran father liked them. My mother really liked them. I’m almost 50 and I liked them growing up and so did almost everyone I knew. And it seems that even today kids generally like their music, even if it’s not at the top of their playlist.
In terms of a broad appeal over several decades, it’s hard to name any American band that’s greater.
(My problem with the Eagles is that I've been hearing their stuff for like 40 years. Their songs are really good, but I've heard them all 87 million times.)