Seeing Jack White play live with the White Stripes was one of the greatest musical experiences of my life. Part of the beauty of their style is that it is built on very simple fundamentals - literally an enumerated set of rules - which form a platform on top of which Jack White can experiment with incredible virtuoso stuff (the best of which is obviously observed in the live performances).
You are 100% spot on though that Jack White isn't famous for this. In their popular singles really only the basic song frameworks, and not so much of the experimental stuff, are exposed. I think it might be some mixture of intentional artistic obscurity, and fitting to the 'radio market' for economic reasons, but either way if you're not familiar with them I really suggest giving all the albums (and some of the live shows e.g. Live Under Blackpool Lights) a deep listen through - really quite incredible stuff :-)
Mayer is an amazing blues guitarist, and recognized as such. He tours with Pino Paladino as his bassist, a testament to his own chops!
And Jack White, while not a "virtuoso" has mastery of the rock guitar language. It's not immediately obvious to everyone, but his technique is flawless.
"fell in love with a girl" is an awesome song but not so challenging to play:
https://youtu.be/95HRZ2SLMJk