I find this idea fun, but I've always though of it differently. Klingons suck at everything except fighting. Every time the Federation has gone up against them in earnest, they get fucking plowed. The famous episode with the Organian Peace Treaty has the Enterprise outnumbered by 30 fucking ships. That just show up at the drop of a hat basically. Its not shown onscreen because that would just look ridiculous, but that's more ships in one place than had ever been mentioned up to that point. Recall in TNG the Battle of Wolf 359 was 49 ships. Speaking of that episode, the Klingons were ready to send ships right away and they were said to be flying in to help.
That episode everyone loves with the Romulans where Picard totally owns the Romulan captain? Who shows up the minute Picard needs them to? The Klingons. Most damning of all is probably Yesterday's Enterprise, where even a tricked out fascist version of the Enterprise D gets pummeled by just three ships and the Federation is said to be losing the war against the Klingons. Also this one is just incedental because it was an excuse to reuse stock footage, but in the Kobayashi Maru one ship against three Klingon warships is said to be a no-win scenario.
The Klingons are probably like your local neighborhood drug addict. Yeah, their life is a mess, but they know how to get what they want and need to keep living, and you do not want to get into a fight with them.