I think It's a combination of things.

I agree with the E-Street comment on the HAND tour. Jon tries to be Bruce more than we know (Another Topic).

I think it sorta goes like this..... First off Bobby is an great musician and an excellent vocalist. More than what Jon allows him to show. I actually saw a solo Bobby show by accident a few years back and was blown away. He did a Roy Orbison tribute and he did it with total justice.

(It's only 2 minutes but check out his high vocals - He challenges Jon And Richie)

Bobby made his first appearance during DA in '97 and the '98 tour. He still remained with Jon with solo charity gigs during the Crush and Bounce era... AKA The Big Dogs.

One thing about Jon, he seems very loyal and hates change. Once your in the Bon Jovi club, you're there forever. That's why no talent Gonzo Obie is still mooching around.....

I'm not sure why he joined the HAND tour but the LH tour makes sense. After that point, I think he earned his spot. He's might add a little vocally and with the guitar, although I would never notice the difference.

Maybe Jon was missing Alec's vocals. Maybe a professional rhythm guitar player to replace his parts. Jon's guitar playing seems more like a prop these days except for his solo on Runaway.

I think it's mutual. Jon needs to keep Bobby in his pocket for all his political solo gigs, so he pays him for that and to join the tour. It keeps him fresh.

Jon figures he could replace some of his guitar parts or just add something extra. Bobby has outgrown no talent SSJ and needs work. Maybe SSJ replaced him and now Jon feels obligated to keep him on.

I think it's a progression of everything stated above give or take.