Cost may not be an issue, but we looked into live-in care for an aunt of dh - frail but no dementia - and it worked out even more expensive than a nice care home. Plus there are all the expenses of running a house on top.
Live-in care for someone with dementia, at least past the early stages, may work out extremely expensive indeed. Such a
person will typically lose all sense of time, day or night, etc., and may well be up and down half the night, wanting or needing attention.
So more than one carer will almost certainly be needed, to allow for proper sleep, breaks and time off. From (too much!) experience, people with dementia do often need 24/7 care, by which I mean someone on hand ALL day, ALL night, 365 days a year.
Which is IMO often best provided in a good care home that caters for dementia.
Plus there is the question of good, adequate training. Any live in carer(s) for dementia really would need it - most people with no experience honestly don’t have much of a clue - and I say that as someone who had to learn the (very) hard way.