It isn't necessarily only for the really rich, but you do need to have substantial reserves of money, to care for your loved one at home if they need full time care, because it requires not only the full time carer to be able to afford to not work, but realistically there needs to be money to pay for other carers to come in and assist at least some of the time. My parents aren't 'really rich' it was just lucky that Dad was frugal and put a lot of his money away in superannuation, he and mum bought their house over the years so don't have to pay rent, and Mum now uses Dad's superannuation(which has been re-invested) returns to live off. Usually if you are going to care from home you will also either need the money to pay for the necessary equipment which in Dad's case is a wheelchair, a shower chair, a hospital bed (which is not necessarily needed but its difficult otherwise to make Dad comfortable in bed as he is hard to move) and a hoist. Alternatively if you are lucky some local organisations might help you to source these things and may even find ways to have them donated to you. So yes it is extremely difficult to end up in a situation where you can care for your loved one at home. You generally also need a home that can be accessible for wheel chairs...mum has had makeshift ramps installed in her house.
On the bright side, although this rapid decline may carry on, there are times when it can be reversed. Dad had to be carried out of the home he was originally in when we took him back to our home and he seemed barely conscious...but now 9months later he is able to walk again and is bright and sparky most of the time. Its a difficult issue, because I think the tendency is for the world and especially hospitals to never consider rehabilitation work for someone with alzheimers, as they consider the disease irreversible so whats the point. Many might say that we have prolonged ours and Dad's misery by rehabilitating him back to his current state, but I can't agree when I see him smiling and laughing now. So if you want for him to possibly get better, that would require a lot of hard work, spending a lot of time with him at the home he is now in, and trying to find ways to exercise his muscles (we started off with just standing Dad up for a minute, then sitting him down, then standing him up for two minutes, sitting him down, eventually seeing if he could take steps, with one or two of us there ready to ease him back into the chair if he faltered...and so on and so on...now he can walk down the street again). However it all depends on the individual's condition, whether they want to do the hard work too, or it might be just too painful and distressing for them, or their condition may not be like Dad's and they can't get better (Dad is only 64).
I don't believe it is often possible for a person to get better when they are not at home because they do not get one on one attention 24hrs a day. Unfortunately because of the restrictions to home care as mentioned above, in most cases the terrible truth is that home care is just not possible. You should not feel guilty about this AT ALL, this is not your fault, life is the cards we are dealt, and sometimes we just don't have the cards we need. I have only posted my message for awareness sake, if you have the right cards...you can sometimes win the game and sometimes you dont even know you have the right cards, Dad was in a care home for 3yrs before coming back home. I also want it to be known that despite what doctors say, there can in some cases be improvement in a dementia's sufferer's condition,it depends I think on what kind of dementia they have and what parts of the brain it affects, nonetheless even we know that eventually there will be a decline once more. I would estimate that Dad's improvement currently wiped out approximately 3yrs of decline.
Last but not least as to whether it would be cruel to take your Dad out of the home for visits back home, again it depends on the sufferer...Dad used to love coming to my house for days out of the home, we used to take him out for birthdays and xmas...for other sufferers it distresses them...you will be able to tell from your father's reactions whether this is good for him. When they want it and aren't distressed by having to go back to the home, this is the most wonderful thing to do for them & you.