I don't know but Kid Rock sounds modern to me. I already think he sounds pretty modern and should just stay the way he is. I am not sure exactly what type of modern rock the writer of this question is referring to but I don't think Kid Rock should change anything.
I do not believe Kid Rock should feel obligated to incorporate modern rock stylings into his music. The wonderful thing about being an artists is the fact that you solely get to decide what is best for it. To assume that he should do something or has to do something undermines the point of the music.
Why on earth would he do that? He's a 1990s relic who isn't going to be drawing in much of the way of new listeners. He has a sound that his fans are comfortable with, a sound that sells records and more importantly, sells tickets to his performances. It's a good business plan.
Thinking that any artist should be influenced by anything other than intrinsic motivation is exactly how pop music, and New Kids on the Block were created. If you believe that Kid Rock should go pop, then yes. He should incorporate modern rock style into his music. If he feels that his music is not the same with this new incorporation, he will not like playing it, and his audience will not likely want to listen to it. If you follow Kid Rock's carreer, you may even find that his music has regressed from modern to more classical rock rather than the other way around. It has worked for him so far. Kid Rock should continue to be himself, regardless of record sales. It has worked for him so far, and there is no reason to compromise now.
No, Kid Rock should not overhaul his sound to incorporate modern rock stylings, because he is very popular the way he is. There is no reason to fix something that isn't broke. Changing styles didn't exactly work out for Garth Brooks. Rock should stick with what made him popular and a well-liked musician.