I agree that cost is a factor, but cheap is really only one of many factors being optimized. The actual cheapest design is often some organic looking design that comes out of software optimizer, but you lower risk by using proven designs.
That’s not necessarily the risk being avoided. The customer may be better off, but project management’s risk vs reward looks very different than the customer’s risks and rewards. Get enough stakeholders together and …
So no, people really do regularly reject the cheapest design that fulfills the spec.