I think the reason for the adjustment is that Shiller designed the CAPE prior to SFAS 121 / ASC 350. In the old days, economic losses were recognized gradually.
Today, accounting standards force companies to do impairment tests and dump massive, multi-year non-cash losses into a single quarter. Because Shiller's CAPE
uses trailing GAAP earnings, these massive, concentrated accounting charges drag down the 10-year average far lower than the actual operational cash flow of the
index warrants. Because these write-downs are backward-looking and heavily bunched into single years, they destroy the model's ability to forecast what the index
will actually earn over the next decade.

Actually I think perhaps you've missed the point. They are real losses, to some passable degree of precision. If you (say) spend a billion buying or building a product that never sells, that's a real reduction to your firm's owner earnings for the decade, and incidentally the share's value. It doesn't matter which year they occurred in---a big lump during a recession because you bought it, or little amounts expensed every year because you built it or because under old rules you'd have goodwill amortization every year. The whole *point* of the CAPE ten year lookback is to get some good years and some inevitable bad years in the mix to get an idea of what an "average" period looks like. If you eliminate the very bad years, you eliminate the whole benefit of the smoothing. The big write-offs are critical, since they are so frequent that they are a normal part of business. That's the only reason to use anything other than the current year results.

The only "big" change in US accounting in recent decades is the elimination of mandatory purchase goodwill amortization. This has the effect of making GAAP reported profits higher than they would have been under the old rules. Not only because "valid" worthwhile goodwill never goes away as it used to, but also because most firms are quite skilled at avoiding necessary impairments...you need only move an impaired business into a reporting division with some successful operations, since impairment tests are required only a the reporting unit level.
Well, the other big change is reporting share gains/losses on the net income line rather than as other comprehensive income, but that affects only a few companies materially--mainly Berkshire.

Jim