The Stake President, as noted in what I said before, has written permission from an Apostle or etc. Keys are never handed down, but the permission to act in the higher powers name, can be handed down, either for one specific event or longer.
Just like we can act in Gods name to do the work he has assigned us too, what is taking place here, is the same. That is like when I was in the Ward Sunday School Presidency, I was only a Priest. But when one of the Bishopric was present, I had if you will extended or shared Priesthood authority, to conduct as if I was a Elder; I was, I guess, working off of his Priesthood, I was officiating, but in his name and authority.
That is not unlike Angels or Celestial beings who appear to someone on the earth in Gods name. Even Jehovah in the Old Testament presented himself as God, acting for and in behalf of God the Father. All I know is, it has been done for time eternal, so why not now.
I understand what you're saying but for me this is like saying - No high priest is present so an elder gets a letter of authority to make another elder a high priest. In the scheme of things as I understand it the office of patriarch is higher than that of a high priest. There are other discussions I've read on this on the true role of the patriarch and the stake president. Its more like they work side by side rather than one over the other but that's another topic.
I don't know if this helps, maybe you have heard it many times before, but a Elder and a High Priest hold the same Priesthood, what differers are their callings and what they can preside over. And as we know that changes over time for many reasons. . The Prophet and President of the Church, hold the same Priesthood as a Elder or another High Priest. What is different again, are their callings, or in case of a Patriarch a office.
It is like a human body, each part is important and needed, they need to work in unison to function and survive, the Church and the Priesthood is much like that, except we get to take turns being many parts, for the learning experience and opportunity to show obedience and sacrifice and become more Christ like.
For me the presiding issue is not an issue so long as we know we are truly led by Jesus Christ. Who sits at the front behind the podium are not lords over our souls so there is no need to fuss over it.