Earlier quoted context omitted.
Maybe I'm still living in the 1990s, but isn't the graphics API call to paint a solid 2D rectangle infinitely faster than the call to blt a 2D image to the screen, with possible arbitrary scaling and clipping? Or is everything just natively textures now and we don't even have 2D drawing hardware?
The second.
A non-textured triangle will be faster than a textured one as it can just return a literal in the pixel shader instead of wasting time sampling a texture for each pixel.
However a single texture sample is so cheap on modern hardware that a specialized path for solid colors wouldn't be worth the complexity in a 2D setting. It's fast enough.