Punctuated Evolution is a theory which is about the timing and speed of evolution under particular circumstances. It is not in the vaguest way a refutation of standard evolutionary science.

To see how it came that Darwin and scientists for some time after stressed slow drift rather than sudden change, you have to read up on the history of the development of evolution before (Charles) Darwin. Read about "catastrophism". Darwin stressed a slow uniform process because he wanted to show that evolution can occur without periodic catastrophes completely renewing the world. And it is as certain as any other scientific principle (like the law of conservation of matter) that his model is true. It is also true that there HAVE been major extinctions in the past, and it's fairly intuitive that when ecosystems are not full, there is likely to be rapid change as species diversify to take advantage of the opportunities*.

Similarly, the tendency of species established in ecological slots is to reject change - there is merely the pressure of the constant arms race between predator and prey, so changes tend to be refinements rather than redesigns.

By the way, scientists DO recognise that organisms are designed- but they are designed by the other organisms with which they interact, and with the physical environment, rather than by an external party.