Mark, suppose population triples but prices and per capita GDP stay the same. The people are no more wealthy. In fact they and the economy probably are a lot worse off. But the GDP inflator model you used would make it appear that a) the economy now is three times larger, so b) prices were three times higher before. That is why I think per capita GDP works better.
I take out taxes because they reduce what companies and people have to spend and invest. I admit my bias/belief that government uses money less efficiently. But there's another side to this, too. Governments virtually always spend more than they take in. So they must borrow the balance. That ends up putting huge strains on the economy.
Back in 1925 government borrowing in the U.S. was minimal. Now the U.S. official public debt is nearly $17 trillion and counting. Throw in state and local debt, and I think you have several trillion more. Count off-balance sheet items -- like Social Security and Medicare -- and you may have several hundred trillion more. That's the amount Boston U economic prof Laurence Kotlikoff cites, anyway.
Point is, the higher debt-laden GDP is in large part an illusion. It ignores, or covers up, all the debt that must eventually get paid back, or see services drastically cut. As I don't believe we can possibly pay off hundreds of trillions of dollars in services, I expect huge cuts. That also overstates the value of today's economy, and means the GDP inflator again overstates 1920's prices.
I agree with you 100%, none of this is an exact science -- and Yale was expensive, definitely for its time, and maybe today as well.