Randy, much depends on your father. You are right that he does not need to be living on his own. What your cousin says is not necessarily true. Mom and Dad moved to AL and then a memory unit. Dad lived 2.5 years after the move. With his cardiovascular problem I honestly do not believe he would have lived that long without the excellent care he received that last 2.5 years. Mom lived for over 5 years. Her decline actually slowed after she went into a care facility. I can cite you many examples of those that have lived for years after moving to a care facility. Yes, some do decline quickly but was it because they were moved to a facility?
What you will frequently see is just how bad the dementia really is. It is not a decline but a clear picture of how well Dad functions. At home he is pattering around in his known environment. It is where he has been for years and he is doing what he does using long held past memories. When he moves to a new environment he will lose those long held memories and have to figure out how to exist using new memories. I wish I knew how many times I have been told... Mom/Dad was doing well at home but seems to be lost at the facility. My Dad was one. He could find a bowl, spoon, milk, and cereal. Then he could put it together and call it breakfast. He had done the same thing in the same house with everything being in the same place for over 50 years. Once in AL he could no longer fix a bowl of cereal because had no idea where the kitchen was. That didn't make him any worse... just highlighted his real level of cognition.
Your Dad may not like care givers in his house. They are intruders in his normal routine. He remembers the house but those people are not supposed to be there. Therefore he may try to run them out. My Mom did this and that is why they ended up in AL. Or you might find care givers he likes and he will be very happy at home. Your Dad might like the socialization and activities of the AL or he might not. It's hard to tell. You know your Dad better than anybody.
24/7 in home care is actually more expensive than a care facility. If you want to give it a try I would go with a agency. This way, if there is a care giver that can not come in the agency will replace them and you will not have to make alternative plans. Be sure the agency is reputable and the care givers are checked out. It is very easy for a care giver to scam one with dementia. It might be worth trying it for a while but be vigilant that the care givers are doing what they should be doing.
If you do decide to move him to a facility then take him there a few times to see if he seems interested in what is going on. Be sure to check the facility out. Online ratings, state web sites with penalties and star ratings should be checked, you need to visit the facility at different times a day, and talk to those that have family members there. You might even want to try a respite period to see if it is a good fit. If you find the right facility, he just might be happy and enjoy all that is going on there.
So explore your options and see what you might want to try first. Just know that no decision is final. You can always do something different if the first trial does not work.
I have tried both with my parents, and for them, a facility was the answer. You have to do what you feel is right for now... and then adjust if necessary