Would it be possible to analyze the inputs to claymores wallet and estimate the percentage of mining done by GPU clients over time?
No. That is by design.
Indeed. This is why we are here isn't it?
I loaned a friend a few bucks for a poker game recently. From my wallet to his hand. I busted out, but he cashed. He paid me a portion of his winnings. From his hand to my wallet.
The only people who know about this transaction are those I chose to tell. And there is pretty much no way to confirm or deny my experience. You take it on good faith that my story is true or you assume I made it up.
This is one way money has been transacted for millennia.
Bitcoin brings speed and verifiable transparency to commerce. <- Valuable!
Monero inherits that speed but allows for the privacy we are accustomed to for cash transactions. <- also valuable!
The widespread introduction of third parties into financial transactions is actually a very recent phenomenon starting in the 1970s, and taking off in the 1980s and 1990s. Before then financial transactions were dominated by cash, and bearer instruments. As a baby boomer I am a member of the last generation that actually remembers experiencing a predominantly cash / bearer instrument society first hand. This is very important when introducing crypto currency to people over the age of 60. It is actually very simple. This is like cash that you can use on the Internet is my opening line. The next analogy is Bitcoin is like marked bills Moenro is like coins. They get it in an instant. On the other hand I was walking with a millennial (just over the age of 20) when a pan-handler approached us. His response to the pan-handler was "I only have debit". The cash analogy will fall flat with someone age 20.