Hardly - they enforce the React philosophy more strictly.
In an ideal system, Components receive props, modify internal state, and render idempotently based on these. The PureRender mixin is a way of saying "yes, this component conforms to the above constraints".
Unfortunately, it's not always the case that the naive way of writing a Component will comply with the PureRender restrictions, so it's not enabled by default. It's not difficult, 99% of the time, to alter a Component to work properly with only minimal changes, and they aren't changes that make the Component code more confusing.
ComponentShouldUpdate is a way of applying tree-trimming logic that React could not automatically know. Business logic and the like. When a Component implements componentShouldUpdate and returns false, it will prevent any children of that component being iterated in that loop. Ideally, componentShouldUpdate should just returning a Boolean value from state, rather than calculating it each time.