If the machines are killing people sometimes that is probably a whole other level of risk and I agree not something I would want to touch remotely.
Didn't go well for the jenny. (Though a turbine might have fared better)
Don't power plants have all kinds of potentially dangerous mechanical systems under computer control? Overpressure on a fuel line causing the pipe to burst and fill the building with natural gas, things like that?
Down in the analogue world, random overpressures, voltage spikes, simple mechanical fatigure, etc happen all the time, so you're going to have to deal. I've written reports on why, regardless of what a sensor said, a simple static beam made of nonflammable materials neither a) spontaneously combusted, b) broke Clausius's principle and moved heat from a cold body to a hotter body. But we still checked.
However, I don't trust systems to remain as robust as initially designed, after decades of undergoing constant pressure to reduce costs, make things more (fiscally) efficient, "cut out fat", etc.
Ever had to start maintaining a codebase after the greybeard who made it retired? Did you have any documentation to go off of? Anyone remaining in the company regard it as anything other than a production critical black box?
Now imagine that codebase is an industrial process, with 20 years of growth, add-ons, changes. Probably some mismatching control systems, and god only knows if the as-builts or red line plans for the additions are all correct or rectified with each other..
Maybe, for example, a mechanic tired of trouble shooting an issue replaces the 9th blown burst disc in a row with one he just cut from the mud flap on his shop truck. NBD, the system was only running 5% over pressure anyway and he wants to go home.
Later, this overpressure state backs up through the system and overheats a pump which, considering that it is pumping liquid explosives, isn't ideal. Maybe this trips a temperature sensor and the jury rigged burst disc is discovered. Maybe it doesn't, or the sensor was bypassed or silenced, and the pump explodes.
I'm rambling, but this is a real world example. My point is that these various factors: designed safety monitors like sensors or fail-safes play hand in hand with over-engineered systems as well as the security of the control systems. Any one part of the system should not be allowed to lapse or be less secure with the idea that another level of the system will catch the problem before it becomes life endangering.
This sounds like turning "an attacker may destroy power generation infrastructure and maybe kill people" problem into "an attacker may repeatedly DoS the power generation systems, likely damage it, and still probably cause loss of life by second-order effects". Doesn't feel all that different.
To use an analogy: it's like saying that attackers accessing the company servers remotely aren't a problem, because the best they can do is to keep them in a reboot loop...
One is life and death, another is lost revenue for a power plant.
Of course it depends on the size and location of the power plant, but there are many more small plants that can go offline without causing any significant effect to the grid than there are large ones, and the large ones probably have the resources to be manned 24/7 either on site or from a remote site over a dedicated and thereby secure fibre link.
One take-away from this thread is that not all infrastructure is 'critical'.