Why does the divergence of a QFT's coupling constant under RG flow trivialize the theory if it occurs in the UV but not in the IR?

Why is the former case described as a fundamental pathology that "trivializes" the entire theory at all energy scales, while the latter case is described as simply indicating a qualitative change in the physics described by the theory?

Because of history. The Landau pole was discovered in the 1950s, when renormalization was not well-understood, and even divergences in general were sometimes viewed as a reason to throw out QFT. Landau was personally strongly against QFT and used this as a bludgeon against it. Asymptotic freedom was discovered in the 1970s, when both the divergences of QFT and RG flow were understood, and was a crucial part of understanding the strong interactions, so it was regarded as a triumph of QFT. This history was fossilized and preserved in the standard QFT course, which has been largely handed down from teacher to student unchanged for decades.

In both cases, the theory gets strongly coupled at some scale, and we can't perform calculations reliably. In both cases, we still want to be able to do physics, and usually do this by finding a new set of variables which are weakly coupled. If there is an asymmetry, it is that the new degrees of freedom in the UV case could be ones that weren't accounted for in the original theory at all, while in principle everything in the IR case is contained in the original theory.