"Rough and ready" in the sense of coming from a hardscrabble background, and getting into the occasional fight (though I don't know that they won many of those ... still, they were a scrappy bunch). And rough and ready in the sense of playing dive bars frequented by crooks, prostitutes ... and tourists, of course
. Brian Epstein cleaned the Beatles up for wider public consumption, with the suits and the bowing after performances, etc., which leaves a lot of people thinking that's who they were - that was a very consciously created image, at odds with ducktails and leather jackets they presented earlier on.
The biggest reason the Beatles stopped playing live, according to what they've said, was that they couldn't hear themselves over all the screaming, and so they just got tired of it. Totally understandable. Given their recorded output thereafter, I'd have to say they made a good choice.
If I want to hear blues, I'd more want to listen to Buddy Guy, or BB King, or Albert Collins, or for a more sophisticated take, Robben Ford. And so on. Of course, some of those guys are now dead ... but then again, I won't hold my breath waiting for the Stones to show up at a local venue any time soon.
Personally, I like the Stones for their own rock and roll songs.