I'm led to the conclusion that the reason that family didn't have a key was because Bob didn't want them to have one.
But that presents me with another problem, because I think son-in-law must have had one, the day Bob disappeared. Det Loomis said when Bob vanished, the front door was locked, and JeM 'let' the housekeeper in the back door. Sounds like he had a key, to me. The housekeeper will know, I suppose.
So if Bob didn't want family to have keys, why would he have given one to son-in-law just popping out to the shops? When Bob knew he would be there to let son-in-law back in, because he was staying home to await the housekeeper's arrival?
If Bob planned on going out he might have handed JeM a key - but then he would also have put one in the mailbox for the housekeeper too, as he always had before.
I want to change believe's question around now - from why didn't the family have a key, to why did son-in-law have one?