I think the discussion is conflating two similar, but separate things: Zentradi "war urges" and the idea of Zentradi being "proud warriors". Yes, Zentradi might have the inborn urge to fight and fight, but that does not mean they are like Klingons or other similar things.
If we're considering "proud warriors" in the most literal sense, a few Zentradi are. We have seen individuals like Kamjin and Milia, who derive enjoyment and pride from their successes and kills. Even Britai enjoys a job well done. But you have to have more than that to be a "proud warrior race" like in many SF settings.
To do that, they have to have ritual, ceremony, an ethos, an overriding, philosophical justification for why they do what they do. The Zentradi don't have that. They don't have medals or ticker-tape parades or Veteran's Day. They just fight and fight and fight until they die. Even if they enjoy fighting, the bare fact is that they didn't choose it. While some Zentradi chose a personal pride in their accomplishments, it's hollow if it came from a world where they had no choice.
This is why I find it hard to put the Zentradi and the Klingons in the same boat. Other warrior races have more of a life to them than the Zentradi do. Even when Exsedol tells the miclones that "to do battle is to live life", it seems hollow when there is no glory or honour, just the next battle.
Now, the word "culture" has multiple meanings which muddy these waters a bit. The Zentradi may have a culture if you define "culture" as the day-to-day activities and rules of a group, but Macross defines "culture" as something that contains songs, love, and (relative) freedom. It is set up in opposite to the Zentradi antagonists.
One of the major arcs of the series was the Zentradi discovering there was more to life and moving towards that. On a fundamental level, the human lifestyle and the Zentraedi lifestyle are therefore not equivalent.
Because of this, I think it's better to show Zentradi characters who aren't warriors, to support the themes of the original series. That's the kind of "Zentradi action" I want to see.
Secondly, Macross isn't clear on how much Zentradi "war urges" effect their populace post-SW1. Many of the examples you cite, and other potential explorations, could have other explanations, in whole or part.
*Kamjin gains followers because the Zentradi simply *can't* adjust, but in ways analogonous to humans who leave prison have trouble living on "the outside" or war veterans have difficutly returning to human society. It's not necessarily that they always want to destroy, but that they just can't, for personal reasons, deal with a world that is so different from the one they knew, even if they *thought* they could.
**Being naturally-sized could be outlawed because of danger that stems not from war urges, but from adjustment failures and personal desire to fight. But furthermore, it could have been done because naturally-sized Zentradi just require too much resources to support, especially if they can reproduce at natural size. I can see this being made the law just for a matter of space.
***Some Zentradi stay in the military because they chose to, not because their DNA tells them so. They just like being warriors, and think their people are good at it because of this.
Free will is hard to determine for a genetically-engineered race, but also it's hard to determine for humanity, so there's that. Personally, I think it's contradictory to the themes of Macross, not to mention a bit depressing, to interpret that the majority of allied Zentradi are always going to be hard to handle, or still primarily define themselves as warriors. If that is the case, why tell the story of SDFM?