I have heard this exact thing debated since the late 80's, so I'm not sure what the last two years has to do with it. The fact is, whether there's a real effect there or not depends less on the precise math of the situation and a whole lot of behavioral and psychological factors. Splits goosing the stock price is a real thing that happens. It may be entirely self-perpetuating crowd-mind BS but it does still happen.
Stock split results in much cheaper options, which many retail day traders seem to prefer.
I might argue that a stock split to a cheaper price would increase your volatility due to the above. Though TSLA's current price might disagree with me as I think it's one of the most traded & is by no means cheap for options trading.
> Obviously there has never been a correlation there and even less so now with the wide availability of fractional shares.
Splits have historically caused price bumps, so I think this isn't true.
I guess all I want to say is that it's more nuanced than 'obvious' and is probably an active debate right now for economists, but I wouldn't know more exact details.
The Dow itself is a bit of gimmick in that its value is the sum of all the prices of the stocks in the index. Meaning if Google joins at $120 but kicks out a stock that was $300 then the Dow would go down 180 points.