Intuitively, I guess that this choice is made up because you want to speed up your calculations. However I think that mixing up different functionals may lead to several inconsistencies. Among the few cases in which this choice may be useful is optimizing a structure with DFT and then using highly correlated methods for refinements. Anyway I would suggest to first running your optimization with PBE and then reoptimizing the structure with B3LYP using the first optimized structure as a good starting guess.

I think it depends on what properties you are going to calculate. I agree with Roberto that if you would love to find the optimized structure from hybrid functional you could optimize it first with PBE then hybrid functional, with this method you could get an optimized hybrid functional structure much more quickly. So, if the properties you are going to calculate are related to structure ( lattice constant, phonon. etc) and you would love to get the hybrid functional structure, I think this is the solution. However, hybrid functional does not always give a better structure. In my research, for example water aqueous solutions, hybrid functional is not guaranteed to give a better structure, but it will give better electronic properties. In this case, the structures from PBE (may be other functionals) could be used to get structure with hybrid functional to get electronic properties.