I think they should continue under another name. Linkin Park just isn't Linkin Park without Chester.
Mike has earned his stripes,I got huge respect for him since he did "Hands held high".It would be a shame if he doesn't continue singing,and same goes for the rest of the band
Side note : Of course I (as a fan) would love to sing with Linkin Park . I knew Linkin Park lyrics before I knew how to read,but as a younger female I don't think I would fit with the rest,and I'd never be able to fill Chester's shoes
Whatever the band decides to do,I'd still be a fan.