With stocks and ETFs, it's more complicated. The exchanges and brokerages will mechanically lower the listed share price on the ex-dividend date. But that's just an artificial beginning.
Once trading starts, all bets are off. Market demand, world news, company/industry news, and what I call "price memory" take over and the results are totally unpredictable. At the end, it's impossible to tie that day's closing price, not to mention the price on subsequent days, to any permanent impact of the dividend. If it were a rigorous science experiment, it would not be possible to conclude any degree of causation.
And yet, that is exactly what anti-dividend folks claim to be the case. Hence the frustration some of us experience.
By "price memory" I'm referring to the collective awareness that investors who frequently watch and trade a particular asset maintain about its price range. They know its 52 week highs and lows, they know where it's been last week or last month, and they have their own personal entry and exit points. These factors cause the drop on ex-date to be quickly absorbed by other factors.