Beyond the answers people have provided, I'd like to add that there is a social element to it as well. Many/most programmers have forgotten math like LA and calculus, there does tend to be opposition to using math at work. Will other people be able to understand your work if you solve it with applied math? Will your coworkers be willing to admit they don't understand your work? And so on.

Of course, this doesn't apply to domains where math is necessary (graphics, etc).

I remember in one engineering job I had, two engineers were tasked with the problem: Given an ellipse, assume a horizontal/vertical line "cuts" off the ellipse. What is the area of the remaining piece?

This is a standard Calc II problem, and I'm sure everyone there had taken it - we required a MS in that team, and some people had PhDs. The solution takes a bit of work but in the end you'll have an analytical formula with the exact answer. In code you'd just put one line with the formula.

Is that what they did? No. They wrote a program to approximate the area. I really doubt they took care of any floating point subtleties, but I knew that I wouldn't be popular if I probed their solution.