Why can't he just strangle or suffocate himself? Durability doesn't stop that.
I think Kaido wanted a spectacular death / fate like the one of Roger / WB had, a fate that would shake the world!
My guess is that he probably learned " something " about Joy Boy and all these grand things he will do, things that will shake the whole world like starting a massive war that would bring the WG down:
He said to Yamato, that there was a reason he chosed Wano as his base of operations
He maybe learned the " where " and the " when " but not the " who " so he thought " well i'm gona stay here and beat the sh** out of everyone " at worse i'm gonna have a fight to the death against the greatest of all ( Joy Boy ) or become Joy Boy himself!