Whe he was at his peak (especially in 1968-70), he epitomised cool.
Now, at the risk of offending any women here, "cool" is something that only a male can understand (when talking about a cool guy. Cool women are another story). Just as women have a bond of sensitivity (sisterhood, whatever you call it) which men cannot fully grasp, "cool" is an exclusively male construct.
There is nothing sexual in it (unlike any woman's attraction to Elvis, or any other cool guy), and it is almost primal with us.
On some level, we (almost) wished we were him - when he was at his best of course, not when he was a blithering mess.
On another level, we wish we could hang out with him, or try to capture a bit of Elvisness in our own approach to women and life in general.