Well, I make no bones about the fact I loved the Queen. So take this with as much salt as you think you need, but I honestly think that there isn't really a better solution than what we have. Queen Elizebeth did not want the role of monarch. She literally prayed to God when she found out that she was in the direct line of succession. She asked for a brother, so she wouldn't have this heavy burden of responsibility.
If we want a single, final, sole, human decision maker I do not see how we can accomplish this without a monarchy that doesn't come with the massive downsides of attracting those that have a lust for power. That the monarchy is essentially toothless in all but the most dire circumstances is a feature not a bug.
It's like the folks in the military that get slated to man the nuclear weapons silos. Very few want the job because they know that they're only need in the very rare circumstance where the whole world is on the line.
It's illiquid power.
As for the rest of it, the holdings, etc. I looked at the Queen as essentially a guardian of nature and an encourager of those in the military, intelligence and of the many charities that exist across The Common Wealth. Yes, she had many fancy dinners, but we got more than what we paid for. Whether encouraging a single little girl to become a doctor when she grows up or slapping a good-hearted wealthy guy on the back when he donates a colossal fortune to helping orphans the return on investment is obvious. Fifteen minutes of her time yielded (and continues to yield) tremendous return.