If your employer really is skeptical, then they can run a A/B test over a small group of engineers to prove out changes in productivity. But not even being willing to run that test when it is so cheap is just management incompetence.

Engineers are ridiculously expensive. In electrical engineering, where the engineers are generally less well-paid than in software, employers routinely spend multiple hundreds of thousands of dollars per engineer per year in tooling. Not being willing to spend 8 k$ on a test of well known technology and attempting to identify mere single digit percentage improvements is just stupid.