A fairly influential philosopher named "Wittgenstein" made essentially this critique 70 years ago. Many philosophers still do conceptual analysis in terms of necessary and sufficient conditions, but few think the project will ever work perfectly for any natural language terms (though a 99% accurate categorization rate is often completely realistic even with only a few conditions). Even fewer think this is the way the brain learns and stores concepts.
Prototype theory is a much better theory of how we learn concepts, but it doesn't lend itself to legal stipulation very well. For that you need necessary and sufficient conditions. So the old Platonic practice still has some value, even if we no longer think the conditions define an objective class boundary or form the core of our unconscious sorting algorithms.
That's not to defend all such analysis. Trying to define "love" or "art" in terms of necessary and sufficient conditions is probably going to be a fool's errand resulting in either a low rate of accurate categorization or a long, unwieldy list of conditions), as was the Gettier-inspired "search for a 4th condition" cottage industry in epistemology. (Though I think some things were learned in the attempt).