Your response has really helped. My reason is mainly that I fear we will lose her as soon as her environment changes. She can walk around her home and knows where everything is. Nothing is out of place and i'm sure the familiarity keeps her from forgetting what I fear she would if in a care home.There are various things to consider I think. First would be your reason for asking! If you want her to stay in her home and you have cameras with 3 of you watching and reacting as necessary, I'm guessing that there are still things you're worried about.
Is the current situation sustainable? Are all three of you in agreement about continuing or is the arrangement starting to crumble?
The issue of falls is complicated! Sooner or later, dementia seems to lead to falls for all sorts of reasons, not least general frailty. You also give the example that your mum forgets what she can't do - my mum was the same after she broke her hip - she just had no memory of doing so. But I'd also point out that mum fell (actually she was pushed by another resident) with 2 carers standing next to her. They couldn't prevent her going down and her hip snapped. It happens. Yes, it would be lovely to have 2 or 3 strong people supporting each and every one of our loved ones 24/7 but that's just not realistic, whether in a care home or their own home.
So I'd say don't base your care home decision on whether your mum would or wouldn't be watched more closely there or at home. Care homes have lots of benefits, one being that there will be staff around at night to assist and reassure your mum, should she need that, which presumably isn't the case at the moment. And often it's that 24/7 company that the person needs more than anything.
Preventing falls is obviously desirable, just not always feasible.
I think perhaps a period of respite may well be the only way to test this out.
Thank you for the detail and be assured that I have taken it all in and will be discussing everything with my 3 siblings, as we all need to be ready if we think the time is right.