The difference between the "equal complexity" argument and your argument is a matter of degree not kind. I don't think anyone believes either extreme of the argument (e.g. I don't think anyone believes that for any reasonable real-valued metric you can possibly come up with any two languages will share the exact same value to the millionth decimal point).

The implicit contention of the "equal complexity" argument is that in fact the constraints that shape different languages are basically the same. Although on the edges the constraints are different, the overwhelming bulk of human experience and emotion is shared among all human populations. Hence we should expect all widely used real-world languages to converge at approximately the same "efficiency." While two societies from opposite ends of the world may seem completely different, compared to the fundamental human emotions that drive the vast majority of communication, those differences are minuscule. Likewise, even though different languages have been around for different amounts of time, beyond a certain time-frame (say several hundred years), they've had enough exposure to the constraint process to also converge on the same "efficiency." Just like any asymptotic process, beyond a certain cutoff additional time doesn't really matter. If you believe in a single origin hypothesis for language development in humanity, then there's an even stronger version of this argument, which is that all natural languages are of exactly the same age.

Hence, another way of framing the "equal complexity" hypothesis is the hypothesis as you make a metric a better representative of true "complexity," the metric is increasingly likely to assign different languages similar scores, resulting ultimately in languages with roughly (but not exactly) the same scores. A uniquely "terrible" (or "excellent") language likely indicates a human society with uniquely different emotions and mental frameworks (e.g. a group of humans who are incapable of getting angry), which currently does not seem to be the case for the overwhelming majority of human societies (various observations of the sort "this society is way more polite than this society" seem like trivialities next to things like "this society has no concept of truth"). There are nonetheless cases on the fringes which seem like interesting exceptions (the most famous is the Pirahã language) and have therefore inspired a lot of controversy ("this society cannot count" definitely counts as a big difference in constraints), but they seem confined to an extraordinarily small sliver of cases (and being so small and little-understood, also have a lot of controversy surrounding them).

Ultimately the "equal complexity" hypothesis is something of an empirical hypothesis, not a theoretical one. I don't think even among its proponents anyone would say it is literally impossible to have one language be more complex than another. Rather the contention is that for languages with sufficiently many native speakers, complexity tends to converge rather than diverge, and moreover this convergence is fast enough that for the overwhelming majority of natural languages, they are approximately of the same complexity.

All that said, in the absence of an agreed upon metric for complexity, there isn't any good way to have a rigorous argument for or against the "equal complexity" hypothesis. From my point of view, the hypothesis is sufficiently vague that I don't expect to ever see a good resolution. For me, the practical point of the "equal complexity" hypothesis is as a rule of thumb to keep in mind that provides an overarching nonrigorous intuition for several observed patterns that do exist across all languages and helps a lot with language analysis and learning (e.g. if one stumbles across a feature of a language that seems very complex, one should immediately be on the lookout for what kind of simple speech and writing patterns it enables, since those are likely to be the idiomatic version of what you're trying to say. And vice versa, if you come across a feature that seems astoundingly simple, think about where it fails and what other circumlocutions could be employed. These two rules alone are astoundingly helpful for developing idiomatic speech and writing in a foreign language.).