According to ENT, humanity barely ventured into space prior to 2151. There were a few interstellar colony expeditions, the first one in 2078, and the low-warp Earth Cargo Service ships populated by the "Space Boomers" and travelling out only a couple of dozen light-years. Humanity hadn't even made contact yet with Andorians or Tellarites. And interstellar war was something they had no experience with; NX-01 was launched as a pure research vessel, and the crew had no idea when they started out that the galaxy was as full of dangerous aliens as it turned out to be. I just don't see any way of reconciling that with an episode claiming that humanity had four wars with a race as relentlessly warlike as the Kzinti before 2070.
Even accepting the animated series as a whole as canonical (and Trek producers have been implicitly doing so ever since "Unification" referenced events from "Yesteryear"), later canon has ignored or contradicted specific episodes or events from earlier canon on several occasions. "The Alternative Factor"'s interpretation of antimatter (which itself contradicted what "The Naked Time" had previously established) has been completely ignored by all subsequent Trek, and the episode has never been referenced. DS9 and VGR ignored how easy travel to the galactic center was shown to be in The Final Frontier, not to mention "The Magicks of Megas-tu." VGR's "Threshold" has not only been ignored and contradicted, but explicitly disowned by its own writer. VGR's "Fury" made claims about the difficulty of changing course at warp that have been completely ignored since then.
So contrary to the myth in fandom, canon doesn't mean every last detail, or even every episode, undeniably happened as shown. A canon pretends to be a consistent reality, but it's really a work of fiction that's being made up as it goes, and sometimes things get rethought, bad ideas get abandoned, new creators disagree with old creators' choices, and new ideas supersede old ones. So there could be entire episodes of Trek that are no longer counted as "real," or that are treated as inaccurate in their details. "The Slaver Weapon" occupies, at best, a tenuous position within canon. If ENT had dealt with the Kzinti, it's certain that any backstory elements from "The Slaver Weapon" -- which were actually taken nearly verbatim from the original "The Soft Weapon" novella and the history of Niven's Known Space universe -- would've been altered or disregarded and a new interpretation presented.
I get what you're saying about canon, but in the case of "The Slaver Weapon", I don't think it's hard to reconcile it with Trek continuity and history, as long as you focus only on what's revealed in this episode and not how the Kzinti or Slavers are presented in the Known Space universe.
The way I see it during the 2060s and 2070s, both the Kzinti and humans are new to interstellar travel and fight with primitive weapons by future standards. Here's a scenario of how I think this could work:
A few Earth nations start building and subsequently launch warp-capable spacecraft. In a relatively short time some of these vessels are attacked by the Kzinti who eat the humans on board leaving only bones in the vessels which are discovered by the Vulcans who report what happened to the Earth nations. These nations, still antagonistic toward each of other as a result of World War 3, declare war separately on the Kzinti resulting in two or three simultaneous wars which each nation wins. A few years later, the Kzinti start attacking Human vessels again. This time, the warp-capable nations form a loose coalition which, with minor Vulcan assistance, forces the Kzinti to demilitarize.
In this scenario, humans don't have to be that advanced or have many ships or go deep into space because the Kzinti aren't anymore advanced than we. In other words, this scenario doesn't contradict things as painted by Enterprise
. In fact, the Man-Kzinti Wars, along with WW3 and the post atomic horror, could partly explain why the Vulcans acted the way they did towards humans in the 22nd century.