Great chart, nice work!
You would have indeed done well investing in oil over the period you reviewed. [Frankly, I believe you will do well for the same reasons in the next decade or two for the same reasons.]
While they might have tracked somewhat at one time, there's no reason to expect what's now a global commodity to track US inflation, especially a commodity that has gone from abundant (relative to demand) to less than abundant or worse. And global demand is increasingly beyond the influence of US demand. So much has changed over the period you looked at.
- In 1914, the US was energy independent and (easily produced) US supply was much greater than domestic demand. Now we import about 2/3rds of the oil we consume.
- We used to have much more influence on oil production (and subsequently prices) in the Middle East, not so much if at all.
- Where US demand once had more influence on world oil prices, demand has increased in other developing countries. Oil prices now reflect world demand, our consumption has less and less impact on oil prices.
- Domestic oil production peaked around 1970, so that's probably a factor in the decoupling you note.