That doesn't invalidate the scientific method
First, the new candidate must seem to resolve some outstanding and generally recognized problem that can be met in no other way. Second, the new paradigm must promise to preserve a relatively large part of the concrete problem solving activity that has accrued to science through its predecessors.
It wasn't so long ago that Einstein declared that God doesn't play dice with the universe. Kuhn doesn't deny the existence of scientific facts or the utility of the scientific method -- he only hopes to illustrate that the notion of scientific truth is contingent on certain assumptions and that these assumptions often get in the way of future progress.
It's also important to remember that Kuhn wrote "The Structure of Scientific Revolutions" back in 1962. At that time, he was largely responding to the logical positivists. While I think a lot of the contemporary rationalist movement is caught up in old logical positivist modes of thought, your own willingness to invalidate models based on evidence wasn't fully developed before Kuhn and Popper brought such thinking into the mainstream.
And to use current rationalist terminology: any given scientific model has an associated probability estimate for being true, which is very close to but not equal to 1; any work built on top of that model will depend on the truth of the model; and invalidating a model in favor of a new one requires re-evaluating any work based on that model. The "giant shifts" you're referring to occur when a model lower down the stack, with a pile of things built on it, gets invalidated or replaced by a better model.
On a day-to-day basis, you don't typically re-evaluate the validity of Newtonian or relativistic physics. Most of us regularly use Newtonian models despite knowing that they don't exactly match how the universe works. And we know that relativistic models don't exactly match how the universe works either (notably on a very small scale), though we don't have better models yet that work on both small and large scales.