I have been to around 15 demos so far (not a lot, I know) and there wasn't a screen on any of them. Although from a safety perspective they are the right thing to do, if a club cannot afford decent video equipment, the screen can render the demo useless, if it is made from cheap plastic which distorts the view.
The insurance isn't there to absolve clubs and demonstrators from their duty to assess the risks and then take action, it's there to cover some of the damage in case something goes wrong despite the care taken. I work in a company where H&S is taken very seriously, because we have accidents every year, and most years somebody gets killed on the job (construction industry). The aim really is to imbue people's thinking so that safety is no longer something you have to actively consider, it's a natural part of how you do your job. Since we work in a similar environment, and the demonstrators are the professionals (not the audience), I would say it is mostly the demonstrator's responsibility to at least give everybody a short lecture at the start of the demo, which may well include advice such as "Be careful when handling my tools, they are sharp". Once said, it then is everybody's common sense that needs to take over, and the demonstrator (and the club) should be off the hook.
Sadly, this subject, similar to many others, is tainted by a few people who cannot or will not accept responsibility for their own actions, and then seek compensation from others for their own stupidity.