They already do this by closing lanes, and even closing entire bridges at night during maintenance when required. The "without notice" part is only if you're doing it wrong - you should be giving your users advance notice of any maintenance activity.
> Every now and then when the tunnel reopened, it would feature a loop-the-loop hidden inside the mountain. While it looked the same from outside, it would therefore become completely impassable by large amounts of the traffic that used to rely on it, including ambulances, food supplies, and the CEO's limo.
I'm not sure I buy this argument. The failure modes of bridges are well understood and usually life threatening. The failure modes of software are not as well understood, but are rarely life threatening. If you're updating pacemaker software, yes, take extreme precautions and don't introduce defects, but the amount of testing and preparation should depend on the impact of a potential failure.
> Every couple of years, your world famous suspension bridge, used as a widely recognised landmark by millions, would be redesigned more like a Roman aqueduct.
This seems like a false equivalency. Suspension bridges take years or decades to design and build. Software can be built in weeks or even days. The frequency of major infrastructure changes is directly correlated with the time and effort involved in deploying them, in both civil and software engineering.