Perhaps the better way to phrase it is that the Wii's GPU did not support normal maps. It did support EMBM, which can look similar, but the effect is more limited when you view the effect of the object from a different angle. Mario Galaxy used a lot of EMBM, and it benefit from having an auto-cam so you would not normally see the effect break. This is why the game may not look as well when you're using free view.
The Wii's lack of modern shader support was likely a bigger barrier to making downports from the other systems than the power was. The Wii U doesn't have that issue.
Did not support? The TEV supported whatever the dev was willing program it to do.
I'm well aware of the natural ability of the GC and the Wii to do EMBM and that it is the most abundant texture effect observed in GC/Wii games, but that is another issue. He claimed that the Wii "couldn't" do normal mapping which was untrue. Even the GC could and did do normal mapping. There are many games that used real normal mapping and even a few that used HDR lighitng which lot of individuals will not accept.
The benefit of the TEV was that it could produce various texture effects with a lower resource cost, so even though the hardware in the Wii was no where near as strong as the PS3/360, it could still produce a lot of the same effects.