Earlier quoted context omitted.
Rare != bad && rare != unimportant. The point of NIST standardizing on SHA-3 is to gradually replace SHA-2 due to the rise of computing power and the likelihood it will become as weak as SHA-1 is now in the near future. Unfortunately, like American credit cards vs. European chip & pin, it's going to take forever to adopt.
No. The "rise in computing power" doesn't jeopardize SHA2. There are important design differences between SHA1 and SHA2 (here's where in my younger days I'd pretend that I could rattle off the implications of nonlinear message expansion off the top of my head). SHA2 is secure; don't take my word for it through, you can find one of the Blake2 designers saying SHA2 is unlikely ever to be broken, or Marc Stevens on a Tw…
So we need to be careful not to use it in setting where that would be problematic. Or we can use it with workarounds, like double hashing (SHA-256d) or truncating its output.
SHA-3 is sponge based, so its output is always truncated, preventing length-extension attacks. So I think SHA-3 is a better default, though it's fine to use SHA-2 if you know what you're doing.