You may not like it, but a lot of machines in history were developed by people who didn't work the math out first.

And even if they wanted to, sometimes the vendor doesn't want to give you (or themselves doesn't have) the information you need to do so. "Just use another vendor who will" you say. Well unfortunately they're the only one whose product meets all these other non-negotiable requirements.

It is truly a miracle that civilization doesn't collapse daily.