"By definition correlation is not causation."
I don't believe that is the case, "by definition", at all.
Consider a company that is able to grow dividends in real terms for a decade.
Without exception, this will see the capital value of such an enterprise appreciate.
This correlation is this case - along with the causality behind it - is patently obvious to see.
"But the correlation between share prices and dividends rises considerably when divs exceed a certain level."
This statement I disagree with most strongly, because it relies on the assumption that the market is dumb, and I think the market is actually very, very smart.
In my experience, more often than not, when the dividend yield on a stock becomes unusually high, then there is a perfectly good reason for it, and that's that because the apparent dividend behind that unusually high yield, is unsustainable.
And the market knows it, and hence starts selling the stock down to a level that actually reflects a more realistic yield that would arise once the dividend is cut.
And my experience is that once the dividend is inevitably cut, the share price falls anyway. Very hard, often.
So I think the exact opposite of what you are saying is true.
And the reason I argue this with some conviction is because I - many years back - had a painful first-hand experience of this when a stock I bought because it was yielding a dividend in excess of 10%... only to have the dividend disappear. [For posterity purposes, the company in question was Southcorp Wines about 15 years ago.]
The saying "if something looks too good to be true, then that's because it most probably is" is very apposite to investing.
(Your rhetorical question as to why the banks are trading at such high dividend yields now, and despite that, their share prices keep slipping, is testimony to the fact that very high yields do not lead to share price performance... in the case of the banks, it's because the market is taking the view that the dividends are to come under pressure.)
Over the years, I have come to observe that it is not the absolute level of dividend yield that matters; rather, it is the growth in dividends over time that is the driver of the share price (which, ultimately, comes down to saying the same thing as it is organic per share earnings growth - from which dividends get paid - that drives share prices.)
(This, based on economic theory that deals with the time value of money, would be particularly relevant during times of low inflation - and low interest rates - which is what looks like will be the case for many years to come.)
And there is plenty of empirical evidence of this:
Stocks that have not exactly been known for their fat dividend yields - stocks like CSL, RHC, RMD, DLX, REA, SEK, DMP, WFD, ARB, REH.... none of these probably ever traded on dividend yields much above 2%) - but that have structural organic growth prospects by virtue of their scale-able business models, have over time performed far better that companies that lack structural growth opportunities, but have seemingly attractive dividend yields, fro example companies such as TLS, and almost all cyclical businesses such as insurance (SUN, IAG), building materials (ABC, CSR, FBU, BLD), media stocks (FXJ, TEN), companies in the service sector (WOR, MND, the various IT consulting companies), and especially retailers (MTS, MYR, DJS and DSH almost always had very attractive dividend yields... until one day they no longer did (and not because the shares went up, but because the dividends went down).
So buying stocks with high dividend yield, and then expecting share price outperformance to follow - which is your theory - is not born out by the evidence.
Quite the opposite, in fact - in most cases, when you buy stocks with unusually fat dividend yields (by association, low P/E's) you end up being little other than noxious value traps.
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