"The essence of strategy is choosing what not to do."- Michael Porter
Everything in testing eventually comes down to one question- how it may affect business, as testing is fundamentally risk driven activity.
As with any effective strategy, an test strategy should not only cover what to test but more importantly what not to test.
As illustrated ...
"The value of any practice depends on its context"
N-wise testing is a technique, not a silver bullet to solve any problem.
It's your responsibility as a professional to analyze how to best approach a specific problem.
Take the example of a pairwise analysis:
valid name, valid password
valid name, invalid password
invalid name, valid password