Why does the Buddha promote the Middle Way for other positions, but does not apply it for his own?

So I've been thinking about how in scripture, Buddha often refers to certain views as the "extremes". A famous example is the eternalists (eternal soul and afterlife) vs the annihilationists (no soul, no afterlife, pure materialists). The Buddha taught both of these as the two extremes and promotes a Middle Way. But is Buddha's own approach not a form of extermism? Consider the following: one extreme that I will call eliminationists (suffering is intrinsically bad and is to be completely eradicated - this is Buddha) vs masochists (suffering is to be sought out and maximized as much as humanly possible). The Middle Way here would be "We do not like suffering (though that does not make it bad or evil by itself), but it has important functions and is in some ways, simply inevitable as long as one is actively "alive" in any conceivable way, so we should seek to reasonably reduce unnecessary suffering as judged by us, but re-orienting the entire society for the sole goal of eliminating suffering can lead to other negatives and extreme behaviour". Why should we eliminate rather than lessen suffering? Isn't that one extreme (other being actively seeking out as much suffering as possible)? I can list many ways in which obsession with harm reduction can lead to a highly dysfunctional society and worsen conditions of many people. So why does the Buddha actively promote the Middle Way for other positions, but does not apply it for his own?