This is excellent advice, unfortunately it's not always possible to stop someone with dementia wandering and can be very distressing for them to try, staff accompanying can work, however I've had backhanders from people who didn't want me there with them, and that of course puts a wobbly person at more risk when they start moving quickly and swinging limbs about. And that's assuming that the staff can be present in every moment with her, 1:1 funding for falls can be really hard to get, and as quickly as staff respond to an alarm, they don't teleport, so there's always a risk present.
And even when present, if a fall occurs, there's certain ways to break someone's fall safely, but grabbing arms or people by the armpits can actually cause injuries to the person and the carer.
The carpets/flooring is an odd one, because every home I've worked in has had hard wearing, easily washed carpets, but although they do help a bit, a carpet won't prevent injury to frail skin, tissue and bones unfortunately.
But checking all of the things in the post I have quoted, and ensuring there's an appropriate risk assessment in place that's being followed is a good starting point.
Unfortunately when people with dementia are mobile, and that mobility starts to decline, there's a period where falls are high risk because they don't remember that their mobility and balance are declining and carry on as normal, it's about the management of the risk of the fall itself, and the protection from injury caused by the falls.