Wow, I just came home from work thinking on this, I remember some band that similar situation It happened like AC/DC and Joy Division. Both with different ends. In my opinion the band should keep going, maybe with another name, with Mike with frontmans, since the style will be slightly different from the current one as it be hapens from cd to cd. And stay Chester's legacy on Linkin Park, just like New Order.
Put Lagacy how the new name this band lol.
Thank you and sorry for my english. Kisses from Brasil :*