If you want to be able to prove hat an item has arrived to a buyer, then yes! It is your responsibility as a seller. It really doesn't matter if you agree with this or not, that is the way Ebay is set up. As a seller you are responsible for delivery of the item, it's that simple. The only way to prove such delivery is tracking(which sometimes isn't even enough) or signature confirmation.
I have had tens of thousands of transactions on Ebay over the years. The carrier's performance is absolutely on the seller.
I am not arguing whether it is right or wrong, that's just the way the system is set up.