Ignoring the morality of it, from a purely economical and financial perspective the cost of elder care for a couple is very expensive, usually averaging around the price of a home, or most of the inheritance. It's basically liquidate the house now to send them to a nursing home, or ask a family member and "pay" them later with the house.

Hence the typical silent agreements that the sibling who looked after the parents before death gets the majority of the inheritance.

Silent, verbal, or even legal agreements are messy though. Talk to family members with the help of a lawyer.

Which one has the greedy attitude if the parents decide "only one of our children gives a shit about me, the rest suck" and chooses to leave it to one child?

Are the greedy ones the other children who say "screw that, show me the money"?

Or is the greedy one the child that says "I sacrificed economically and personally to do unpaid domestic labour, now I'm getting paid back for my kindness"?