Vertex count may be more accurate of a measurement of "mesh memory usage and mesh rendering time", but vertex count is not nearly as easily measured.
Yes, given a specific mesh with all of its attributes, it's easy to tell how many vertices are in it. But how many modelling tools can tell an artist how many vertices a given mesh will produce?
After all, the vertex count is usually based on the topology of the various attributes of a mesh. That topology changes when new positions are added or removed. That topology changes when texture coordinate vertices are added or removed. When smoothing groups are modified to create sharp edges. And so forth.
Furthermore, most modelling tools can't really give an accurate vertex count anyway, since they usually don't store vertices in the fashion that the rendering application will use them in. They tend to store the vertices as individual arrays with individual array indices, which is typically not how the renderer will see them. So most modelling packages cannot tell the user what the vertex count is, outside of writing a plugin to provide that information.
So if you're trying to communicate a limitation to artists, the easiest way to give them an approximation of what they have to work with is to provide a triangle count. Yes, the hard limit is the number of vertices, and the asset conditioning pipeline should certainly reject meshes/whatever that are too big for the available memory.
But triangle count is more useful as a "quick heuristic" than vertex count.