I like the shiller pe but there have been some substantial accounting changes over time that have affected earnings. For example starting in 2001, goodwill no longer had to be amortized which had a positive effect on earnings. Expensing of stock options had an opposite, negative impact on earnings. Im not sure what the net effect of these accounting changes are but all earnings over time are not equal.
More importantly, the concept of the shiller pe assumes a low growth rate in real eps which historically has been about 1.5%. If that level has changed which is very possible given the lower payout ratios over the past couple of decades, then the fair level of the shiller pe would have changed also.