It depends. If you have a large enough team on a project that you can shield someone from math oriented and efficiency sensitive tasks as well as the planning in place to do it then the math heavy analysis isn't needed. Many start-ups have teams of 1-2 working on entire web apps and need everyone to be able to take on any task. Many people without the math background end up writing n^3 solutions to O(n) problems in code that gets executed at high frequency. The core value of those math skills isn't their explicit use, it's the training the brain gets in writing efficient algorithms and having knowledge of how hard certain problems are. Even in CRUD apps I've often seen requirements that are equivalent to NP-hard problems on large data sets, and I've been able to discuss the efficiency tradeoffs allowing the business team to redesign features when they weren't happy with performance. Without the math background, we'd see build it, put it in production and when the data gets large enough cry about performance and lose users waiting forever for a page to load.

The last piece is in many start-ups I've seen the programming team will own or co-own Analytics because of a lack of statistics skills on the business team. Again with a small team not having a solid math and stats background has huge implications on the data analysis portion of roles.