The difference is that Microsoft released consoles with very similar purposes and names in the same generation.
Labelling the Switch as a new version of the Wii doesn't make much sense because it occupies a different niche, comparable to PlayStation/2/3/4/5 vs the PlayStation Portable.
PlayStation's addition of "Pro" in it's own naming scheme clearly distinguishes the more powerful console. Delaying the release of the pro model until later in the generation's lifecycle also helps reduce friction.
I don't think non-numbers are a bad naming scheme, just the simplest. It means its easiest to keep up with and archive, but it can also mean it's hard to tell audiences what fancy new features you're marketing. If the Wii was the Nintendo 5 and the Switch was the Nintendo 7 I'm not sure if it would be quite as snappy in consumer minds.