Why would you care if your company was accessible to the little guy? Those stocks are sold - you never get more money from them unless you issue new stocks, no matter how they are traded in the future. (Stocks seem like a pretty bad deal for the company anyway: get funded via IPO, be forever beholden.)
In fact, they're a liability. So what benefit to a company from increasing the number of people you have to answer to?
If your stock is accessible to more people, there's higher demand, which should drive up the price, benefiting those who hold the stock (and make the decision to split).
"If your stock is accessible to more people, there's higher demand" - this the answer 90% of the time, but I don't believe there has ever been a study (and I've read three or four) that suggests there is any evidence this is true.
To make what I consider to be a not unreasonable comparison, "The standard gold bar held as gold reserves by central banks and traded among bullion dealers is the 400-troy-ounce (12.4 kg or 438.9 ounces) Good Delivery gold bar." [1] - that gold bar currently sells for $41,260 [2] * 12.4 or $511,624/bar. There does not seem to be any difference, per ounce, in price between a one ounce nugget and a 438.9 ounce unit (indeed, there seems to be some transaction costs that imply the larger bar is less expensive per ounce)
For a mature company that is throwing off lots of profit and cash , there are a lot of investors who are analyzing the Discounted Cash Flow of that company, and paying for the stock based on that number. Apple, for better or worse, has entered that realm. Therefore, if they trade significantly below their cash-flow value, those investors will buy up the stock, if they trade significantly above it, those investors will sell the stock (or short it if things get too far out of whack) - It doesn't matter if the stock is selling for $100, $1000, or $10,000/share.
But, the people who run Apple have access to the best advice that money can buy, and they have made this decision - what I'm interested in, ideally from someone who has worked behind the scenes in this kind of really-big-company stock split, is the real reason why this is done. I have a theory it's a mechanism to reward bankers with a lot of business with useless make-work, in return for getting positive ratings moving forward - but I'm open to other theories.
[Edit - another Theory is that Tim Cook and/or his CFO Peter Oppenheimer are just fed up with being asked about a stock split, and given that the stock split is an absolutely meaningless event, that has no negative/positive impact on the company value, but will eliminate the ongoing nagging of people about it, just decided to eliminate that annoyance. My counter argument to that would be is by giving people something meaningless to complain or ask about, you distract them from other things that you would prefer they not spend so much time on - so it's good to leave a few of these around as decoys.]
We can't really get into Tim Cook's mind or his advisors' but whatever their motivation is, it's not guaranteed it's very rational or scientific.
As you note, what matters for a company's valuation is the discounted (present) value of all their future cash flow (+ their book value). Unfortunately no one knows what that number is because no one knows what the future cash flow for AAPL will be. People know the history, the reported numbers, and they make guesses about what the future value of the company will be. There aren't many business where you can predict with any degree of accuracy into the future and Apple specifically, unlike someone like Coca-Cola, isn't in a very predictable market.
Even if you could predict AAPL future cash flows very accurately you would also need to predict future interest rates to be able to set a multiple on those cash flows to esablish a valuation.
To conclude, just because a lot of investors are "betting" on AAPL doesn't necessarily mean that its share price is a better estimate of its true value. If the market collapses tomorrow AAPL is going to fall just as quickly as the other large and small stocks. No one is going to care what those analysts predict the future cash flow will be. What is true is that it is a lot harder for people to manipulate the share price compared to smaller cap stocks with smaller volumes.
I don't think the analogy to gold is strong, mainly because any holder of 400 oz t gold bars can freely convert them to smaller units, the old-fashioned way. You can't do that to a BH share certificate, or at least it doesn't work as well. ;)
While it's not a 100% analogy, it's 99.99% - Good Delivery gold bar are virtually never converted to smaller units. Indeed, it's rare that they are ever even moved from their vault (though that does happen on occasion).
The point I was trying to make is not that Gold Bars are impossible to make smaller, but that their very high price "per unit" doesn't result in any lower-prices per ounce than if they were broken down into smaller units. I.E. There is no pressure to reduce the size of Good Delivery Gold Bar's - the market realizes that just because they are expensive per unit, it doesn't reduce their price per ounce.
In fact, they're a liability. So what benefit to a company from increasing the number of people you have to answer to?