Citigroup's Director of Equities put market P/E ratios on the x-axis, whereas you put CAPE ratios there.
P/E and CAPE are not the same thing!

No argument, I didn't mean to suggest otherwise.
I don't look at trailing-twelve-month P/E ratios as a market valuation metric because they have close to zero predictive power. Sometimes earnings are depressed meaning a seemingly high P/E and the market is a great buy, and vice versa.

Can you use the market's simple P/E ratio to time the market over the next 1 to 3 years? No
Sounds right.

Can you use the market's simple P/E ratio to plan your retirement which is 10 years away? No
Sounds right.

Can you use the market's CAPE ratio to time the market over the next 1 to 3 years? No
Sounds right. One possible exception: when CAPE shows the market to be very cheap, it generally works out well quite quickly. That's rare, of course.

Can you use the market's CAPE ratio to plan your retirement which is 10 years away? Yes, if you believe the post-1996 results will continue.
Reasonable. Though nothing about 1996 is special...though it can't give you specific numbers, high CAPE values lead to poor forward results pretty reliably, and vice versa. Both pre 1996 and post 1996.

Is there a correlation between CAPE and forward 10-year returns since the early 20th century (120+ years)? No
Well, that one is false. The numbers go up and down together, just not perfectly.
Around the end of 1929 CAPE was high (even after the crash), and the next 7 years were negative in real total return.
By end 1931 CAPE showed things to be cheap, and the next ~7 years returned almost 12%/year in real total return.
And so on.

The main thing is to appreciate is that the 20th century was a period of gradually rising valuation levels. If you adjust for that, the match gets a lot better. Without a doubt, the pile of cyclically-adjusted earnings you're buying for each $1 is the single biggest determinant in what your returns will be in the next 5-15 years.
What are the failures as a predictor, even after adjusting for slowly rising valuations? Mainly three.
* Returns starting around 1950s were higher than you'd expect, because valuations were so high in the "Nifty Fifty" 1960s era, around when Mr Buffett closed his partnership for lack of good investment prospects.
* Returns starting in the early 1970s were a lot lower than you'd expect, just because things were so darned cheap in the early 1980s.
* Starting from the early 1990s the returns were a lot higher than you'd expect, because valuations were so extreme around the start of the millennium.
But other than those stretches the match is darned good when scaled appropriately, squiggle for squiggle. If you assume, as seems reasonable, that valuation levels at the end of a decade will be neither wildly high nor low, the cyclically adjusted earnings yield can given you a very good guide to what you ought to expect as a return.

Unfortunately nobody can predict whether valuation multiples will continue rising from here, stay about the same, or fall back in the direction of the old norms. But I guess we can't look at the old data and pretend it didn't happen.

Jim