I think the general consensus has been that the word pixel is morphologically flexible enough -- more than given appreciation for -- to account for what makes sense accounting for by itself. The name makes a distinction that makes sense having in many ways, that is distinguishing computational era of this medium logic from the non-computational era, and the particular possibilities in workflow that means. In that, it makes no sense discussing this as one name being a replacement for the other, on the thought that pixel art would be obsolete because it's all the same in a better name, but rather together describing a methodical hierarchy of on-going evolution and specializations: given two works of art, both may have a grid in common, but one of them also is pixel art in specific, while the other is not, and that's worth pointing out.
However it is rather peculiar that a cross-stitch can look more like pixel art than many a modern digital art using pixels looks like. The introduction of painterly workflow into pixel art came much later; in the very beginning it was just setting pixel by pixel. And over time, the more painterly the emphasis of tools, the farther it became from looking like the beginnings of pixel art, until forced calling it different entirely, despite made of pixels. Thus it stands to reason that a workflow that is not by-pixel of any given resolution, is muddying the primary nature of what makes this art distinctive most from any other art, and by this creating merely an artificial difference within itself and to its past of any era. Pixel art is more different from cross-stitch, the less pixel art is purely pixel art-ish, so to speak, given the computational possibility of using the same underlying logic of medium in a way that's more akin to a different art.