Why didn't either of the Klits go after Valuev's belt?
They both did.
Wlad wanted the fight, but "settled" on Chagaev, which made more sense since he beat Valuev, and such a match determined, for all intent and purposes, HW supremacy.
Vitali wanted the fight, but instead accepted the Haye fight... only to have it rescinded when Haye instead stepped to Valuev, leaving Vitali to face Arreola.
The better question might be, why didn't Valuev go after either of the Klitschkos?