Sure. Pick a specified load at a specified time and the engineer's job is to build the cheapest possible bridge at that load and time. Raising the safety factor doesn't change the objective function. The objective function is still "cheapest within spec."
This is why bridges are not just huge chunks of titanium. Those would work very well at handling 50 tons at year 70, but would be shitty bridges because they are too expensive to build.
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.