When Curzon Dax was the UFP Ambassador to the Empire, he became godfather to the son of a prominent military commander (namely Kang), who held enough power in the Empire to play a key role in negotiations between the two governments. That friendship led to a Blood Oath and lasted over two lifetimes.
Picard played a pivotal role in appointing the previous Chancellor, and he was more than a little bias--having negative feelings towards Duras, who appointment would most likely have damaged/destroyed Klingon-Federation relations.
Fostering good, personal relations between the Federation and Klingons would be key to ensuring stability between them. Worf being in Matrok's House would probably put him in a better position, being a metaphoric bridge between his status as a UFP citizen and the Klingon Chancellor.