They're all primary writers. Brian writes a lot/most of the songs when he's in the band, but the other guys all write as well, specifically when Wilson is off Wilson'ing.
Mike Love owns the rights to 'The Beach Boys', so he can pull shit like this. Love would also rather play Kokomo with John Stamos, whereas Wilson would rather play obscure songs from their obscure albums - two personality types that are hard to meld.
Love will probably tour with a hired band, as the Beach Boys, and Wilson will probably tour under his own name or as te Beach Boys Band. Jardine may play with him.