quantum field theory - Divergent bare parameters/couplings: what is the physical meaning of it? Do this have any relation with wilson's renormalization group approach?

I understand that bare parameters in the Lagrangian are different from the physical one that you measure in an experiment. I'm wondering if the fact that they are divergent has any physical meaning? If they weren't the divergencies that arise in loop calculation cannot "be put" anywhere else. I'm OK with them being different from the physical one, but why is it OK for them to be divergent?

EDIT: I have some difficulties in understanding if this has any connection with renormalization group approach of Wilson. They seems to be quite different. In fact in the last case you start with an effective field theory valid up to scale Landa (sharp cutoff) and you "integrate out" the high momentum part of the action to see how the theory behaves at low energies. On the other approach you want (after the renormalization ) to let the cutoff go to infinity and find finite results. That means that the theory is not sensitive anymore about the high energy/short scale behavior.

The running of the coupling in Wilson's approach has nothing to do with the bare parameters going to infinity when the cutoff is removed right?

Is there any reference that tries to unify this 2 different approaches? I read deeply this two books: Quantum and statistical physics - le bellac Field theory, the renormalization group - amit Do you reccomend any other books/articles?