Monetary Communism is nothing more than another version of Capitalism - a monetary based system regardless of how you put it - basically a variation on the theme (which is exactly what the Nazi's implemented back in the day - it certainly wasn't 'moneyless').
But fundamentally speaking, Capitalism (or any monetary system) is unsustainable (any system expecting infinite growth on a finite planet is utterly idiotic - not to mention that the pursuit of profits and competition don't do terribly good things for progress - most relevant scientific breakthroughs that forwarded science itself in a meaningful way came from cooperation, not competition - couple that with the notion that money=debt, and you basically have a recipe for disaster - the system is self-defeating and is epitome of inefficiency and incremental technological revisions [not actual breakthroughs or quantum leaps] because its more 'profitable' in the long run).
As for modern day Klingons - well, we've seen some Klingon scientists, but I would have to concur that given how they were perceived in Archer's time, one wouldn't necessarily expect them to be terribly advanced - plus the overall mentality of constant blood-thirst, conquest, wars and conflict that was pushed in a stereotypical capacity is fundamentally unsustainable/unworkable (if EVERY Klingon was like that) - then again, they would probably have to acknowledge the need for doctors and scientists who basically keep everything running (or at least, start everything up - because in order to reverse engineer hur'q tech, they would have to use scientists, engineers, and the likes) - although, this could be remedied if everything is automated (but the writers weren't THAT in tune with technology to begin with) along with self-maintaining machines, machines building machines, etc.
WE already had this technology for some time in the real world... one would imagine Trek universe (the Federation, Klingons and Romulans) would have it by default (any space-faring culture would probably have to implement large portions of automation as a basis because manual labor simply wouldn't cut it at the levels we are talking about - especially if they have any degree of 'sustainability' in mind.
This is why Humanity did it right by eliminating money in Trek. When you do that, you basically get rid of fictional monetary restrictions and focus on what is achievable from resource/technology point of view, keeping in mind sustainability and achieving abundance at the same time (and when you switch to superior synthetic materials - which can be produced in abundance - you basically get a lot higher levels of technology by default because you aren't using materials that are 'cheap' and 'inefficient').
Anyway, one would think while Klingons may not hold scientists, engineers, doctors, etc. in the highest regard... that doesn't mean they wouldn't have or use them.
The warriors we've seen are basically an equivalent to a military that knows how to operate the ships and conduct repairs (even though it could all be automated) - so, from a cultural point of view, they might not view scientists in a good light, but they also know they need them (to at least invent new things - although AI's as seen in Trek would be able to improve upon existing technology on their own to a decent degree - whereas higher levels of creativity might still be delegated to living individuals).