What are the downsides of having an inter-generational safety net?
Changes opinions to be against estate taxes (my family earned this money why do you get to tax it)?
Establishes expectations of inter-generational help or wealth?
I'm not sure I see even one argument against the safety net specifically. A semi-argument seems to be that a familial safety net will somehow reduce other safety nets, but that sounds like a false dichotomy at best.
Slightly off-topic, but in recent memory: The woman from Alabama who joined ISIS had experienced poor family relations and is now stuck in a refugee/detention camp in Syria. Because of the poor relationships, her ignorance in Islam and ISIS enabled them to turn her to support their cause, which she seems to now renounce.