My perspective is that a great example of designing without first principles thinking would be designing a better hammer.if someone told you that you had to design something to knock in nails then most often using something ‘like one of the hammers at Home Depot‘ as analogy works rather than starting from scratch and pondering the nature of nails and wood in your particular state and situation and etc. But in a market scenario if you happen to design a better hammer which is unlikely you get a big payoff but most likely you fail to notice something surprising. The more formal coding of this is parametric (1st principals) vs non parametric (analogy). it’s the difference between predicting 2030 vehicles by guessing rather without reference to other examples what the regression shape is vs. finding say that Ford had a very similar pattern in 1908-1911 as you did in 2018-2020 and going with that.
The existence of a hammer is admission of a problem with a failure of nail design. The concussive nature of the hammer is not the problem to address even if the market would happily reward a marginally improved hammer. The first principles effort should pivot around why a nail requires a hammer or even better why a nail is needed at all.
The existence of a nail and hammer is an admission of a kind of failure of joinery. It could be viewed that first principles thinking would result in the elimination of nails at some future point. This would be disruptive to certain industries and perhaps lead to further improvements in shelter etc.