Why losslessness requires voltage and current must be both zero?
I think the point is that we cannot measure the energy inside a component but we can only empty it and sum up the energy flow at its terminals.
From an electric point of view it's like a black box with an interface.
So, at the end of time we shall have:
Net energy zero,  w=0
No energy inside,i.e. state variables at zero, so any v=0 and I=0