There's a great Acquired podcast episode about Warren Buffet and his obsession with compounding returns. After listening to that episode, it totally makes sense why he'd be opposed to a stock split.
I highly recommend it for those curious about Buffet
"[S]ignals the power of compounding" -- only to unsophisticated (frequently, retail) investors. Institutional investors always have historical data that is split-, and even dividend-, adjusted. If I had to guess, refusing to split is like a form of virtue signalling, nothing more. When I was a kid, IBM usually had a high stock price, over 100 USD. I never understood why; nor did my father, a stock broker.
"Unsophisticated" investors see the big number and the price history (which is much simpler without splits) and see the power of compounding plainly. There's not much more to it than that.
A common misunderstanding is that if a bunch of investors pool their stocks, they’ll earn more compounding interest on the larger pooled principal than they would individually, or conversely that a stock should not be split or it will earn less interest.
The continuously compounding exponential return formula is
P(t) = P0 e^rt
Note that only time enters the argument of the exponent, not the principal. So the returns are invariant to divisions of the principal (ignoring human behavior effects).
I highly recommend it for those curious about Buffet