There are plenty of reasons why engineering isn't "agile" and it's only usable in software development, and one of the main reasons is that software development projects manage a single resource: man/hours. Building the wrong or inadequate solution has its cost, but rebuilding something from scratch does not require additional resources to be allocated to the project: just keep the same team working on it and results will pop up.
Engineering projects are very different than software development projects. Materials and components are the driving cost of a project and there are plenty of stuff that must be done right from the very start. It's unthinkable to scrap a machine or building or tunnel midway through, and it's inconceivable that some disaster happens at all. Engineering either gets it right at every single stage of a project or there are serious consequences to deal with, which in some cases might even be criminal charges. If for some reason a prototype crashes during development then the project might be forced to shut down.
Just to pick a few nits, actually bridges are indeed tested during and after construction. It used to be standard practice to do test runs with near limit loads to inaugurate bridges, consisting of getting a fleet of military vehicles or water tankers to cross the bridge while surveyors monitored the bridge's response.
Nowadays non-destructive testing techniques are favoured for a number of reasons, including the fact that sensor rigs can also be used throughout the structure's lifetime to help determine its fatigue life.
In the macro view from 10000 meters high, it's always the client that pays. Even if he gets away without paying once, he'll pay it back (and more!) in stuffing on other projects. Because without that, the service provider goes under.
Of course, occasionally, inexperienced service providers that do not stuff their projects do go under. This puts evolutionary pressure on the ecosystem so that the surviving service providers are selected over many such trials to know to stuff projects and invoices.
Honestly, in these cases, there's nothing better than waterfall, partly to save development time, but mostly for contractual protection: If a small change can cost millions more (and from experience, they can), you need to know who is responsible for paying those millions...