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.
That being said, I agree with you wholeheartedly about the benefits our current system affords, though there's precisely ZERO reason those functions need to be performed by a monarch. There are other ways to achieve the same results without needing to prop up and pander to the spoilt, entitled children of some long dead yet highly effective murderer.