When have politics ever solved problems?
I can understand the need for it if you live in a world where most people are lacking in education, but if you educate the entire population with relevant general education from the get go, you wouldn't have a need for governments in the first place because the notion falls apart at such a prospect (people are capable governing themselves and form cooperative unions to work with others on various projects - having a system of access abundance gives you the necessary resources to accomplish various things and solve problems - in a monetary system, this is restricted artificially due to money, even though we have been producing abundance for a long time now).
This is why the notion of governments in the Federation is relatively absurd (because it was implied that everyone would be exposed to relevant general education).
Although, to their credit, I think the writers wanted to make things similar (a bit mistake), and attempted to portray people in positions of power as such who are not prone to being corrupted (because they couldn't envision a society without governments without thinking it would 'inevitably' turn into an 'anarchy' - which is utterly absurd).
However, I can see the government surviving within the Klingon empire. Most of them conform to the notions of combat, glory, honor, etc. Very little relevant general education in the population.
If you noticed, Klingons exposed to Federation values/ideals and even education do not seem to conform to the notions regular Klingons do.
Even Alexander who essentially grew up in the Federation, never really lived up to the status of a warrior (given his 'performance' in that area and only joined the Klingon task force to impress his father mostly) and was hardly bloodthirsty and whatnot.
Worf is a different story - he was a kid that was already ingrained with Klingon cultural values, and as such decided to pursue them on his own vigorously, but as time went on, he also showed less and less of an appeal for combat like regular Klingons.