The problem with a CB/BB hybrid is that the tasking for each is pretty much mutually exclusive. Modern ASCM also mean that the role of the BB is effectively removed from the battle space, they are now a pointless, expensive ship. Eventually it will be the other way around, BBs will once again offer something no one else can, but that may have to wait until space.
As for a shore bombardment, they have that already! Every single CG or DDG in the USN has a 5" gun, which is what is used for NGS. The big 16" guns were ship killers, not for shore bombardment, except in certain cases where it was used to bust hardened targets or lower the crest of a mountain 100'. 5" guns are more than enough for NGS, they have a higher rate of fire, integrate better with other ships and overall are much cheaper to run.