I completely agree with you, personally. The problem for a mod in my position is explaining to other players why a player should be allowed to use a PB who's died recently or continue using a PB without changing, since these are conversations that actually have come up a couple of times recently. But you're completely right.
There was a meta discussion in a RPF community a while back about that - whether or not it's disrespectful to continue on with a celeb line as an AU or do past plots after the person in question has died.