I always assumed (but have no way of knowing for sure) that was also partially influenced by the line in "Errand of Mercy":
I forgot, but remember this now. But I wouldn't say they were quite friends by TNG. More like a mutual agreement to end hostilities, than anything. The Klingons still seemed to openly view humans with a certain amount of disgust, or that they were inferior. Not to mention how quickly they were willing to go to war against the Feds in DS9, simply because the Feds wouldn't sanction their invasion of Cardassian territory. And then there's the renegades that always pop up, like the House of Duras, from alliance with the Romulans, to Klingon Civil War, and destroying the Enterprise-D.
Then there is the simple fact that they are an Empire and not a Federation, and their culture is based on blood lust, which is totally incompatible with almost everything the Federation is supposed to stand for. And the Klingons showed that they had changed little from Enterprise to the TNG era. They didn't WANT to change. Other than the Praxis moon exploding, the Klingons had no reason to cooperate with the Federation. It seems that using the example of the E-C falling in battle was more a propaganda campaign, as well as the Battle of Kittomir, to justify an alliance with the Feds (or more properly a cessation of open hostility), than an actual change in Klingon culture. The DS9 Klingon-Federation war demonstrates that.
Like I said; lousy allies.
With the Vulcan/Romulan lifespan, there could have been Romulans living up to the TNG era who were actually around during the Earth/Romulan war. So while it's a historical thing for the humans, the Romulans who actually lived through it might be less likely to want to ally themselves with their old enemy.
That is a plausible explanation, but it also could apply to the Klingons, too. While not quite as long-lived as Vulcans and Romulans, they are pretty close. Kor, Koloth, and Kang come to mind as having lived longer than a century and a half.
Replace the concept of honour with the concept of morality, and I know a lot of humans like this, too.
True, but with Klingons, it seems truly honorable Klingons are the exception, not the rule.