My mom wanted to avoid probate at all costs and had all 4 of us as beneficiaries on everything including a TOD deed on her house. When I pointed out that getting all 4 of us to chip in to pay her funeral costs and the bills at her house, she open the account I am on and put enough in there to cover those things. Yes, I could be dishonest and keep that money for myself, but I would never, ever do something like that and she knows it.
I don't think parents and certainly not the other beneficiaries expected what happened to occur. You never know what a person may do when they come under the influence of a dishonest significant other and/or friends or have financial difficulties or begin having mental problems or get involves with a religious cult or ... I have a number of 65+ single family members whose behavior is so irresponsible that I suspect they are in the early stages of dementia; they are placing themselves in unsafe environments and at great financial risk for their futures. They are not so incompetent that they must have a guardian; by the time they get to that stage, they will be destitute and will have alienated the younger family members who rightfully have become frustrated dealing with irrational and obnoxious elders. Even some of the junior family members are totally oblivious to responsible financial management and planning/saving for their futures.
I think one of the important decisions if a person wants to do what your mother did, is to make sure the responsible individual has shown good judgment in their personal and financial decisions and is independent of outside influences. If the responsible person consistently has financial problems, there might be the temptation to "borrow" from the elderly person.
Why do you not prepay the funeral costs? It is one thing you can do and still qualify for Medicaid if necessary. With the cost of long term care, planning for needing Medicaid for all but the very wealthy should be considered.
I am also very much in favor of a person making their own decisions about their funeral/memorial service if they even want one and their obituary. Our family did not do this and the person who ended up making most of the arrangements went overboard on the flowers, etc. The funeral ended up costing about 3 times what was planned for. As a note, that person then complained about how much they got from the estate.
Actually, the best advice ever came from FIL who saaid "Beiong of sound mind, I spent it all."