(I work on React.) This isn't quite right. If we recommended that PureComponent be used everywhere, it would probably be the default already. Rather -- the comparison to decide whether or not a component should be rerendered costs something, and in the case that you do want to rerender, all of the time spent checking whether you should have rerendered is wasted.
Instead, we'd suggest you be conscious of where you need to do the comparisons. It's usually only in a couple of places in your app. Good candidates are on the children of a long list or around large parts of the app that change independently (that is, cases where you know the parent should often rerender but the child shouldn't). A few well-placed shouldComponentUpdate (or PureComponent) uses can go a long way.