The trustworthiness of the family members (and their spouses) matters a great deal. When my mother died the security people at the building immediately changed the lock because in the past what had sometimes happened was that relatives with keys raided the apartment for valuables. This gets the building owner involved in lawsuits for not taking reasonable measures to preserve the estate. They would give me a key only after I had the Letter of Administration.
Fortunately those issues did not come up with my family, but I can see it coming when FIL passes - one SIL has some severe mental issues.
The fact that I had been handling Mom's finances for the six-month period before made administration a lot easier since I knew where everything was. Also I was joint on her bank account and could pay the immediate bills, and was joint on the safe deposit box so access to that was easy too.
I heard the call to do nothing. So I answered it.