The math can work out in some cases. I've had my 400$ Allen Edmunds for 8 years, some wear, but generally still in fantastic shape and very comfortable. Prior to getting them I bought 1-3 pairs of ~70$ department store shoes per year.
Usually it's very anecdotal and hard to tell ahead of time. My current shoes cost 40€ and that was about 4 years ago. So they have lasted atleast half as long as your expensive shows for 1/10th the price.
I have some inexpensive Chinese-made boots that are over a decade old, I think. It can't be the norm that shoes last 4 months, unless you are talking about wearing down the soles of running shoes.
