Your analysis depends on these magic companies that experience continued above market average compound dividend growth, right? For 30 years?
I think this is a flawed assertion.
Eventually those companies would by definition, comprise essentially the entire market.
Can somebody do the math? It reminds me of the St Petersburg Paradox.
My analysis doesn't require above market average compound dividend growth. I do however prefer an earnings yield of about twice the 10 year federal bond rate.
In my dividend growth portfolio I don't try to beat the market. I try to get the best risk adjusted returns possible using using a strategy that fits my personal situation. There is more than one road to Rome. In order to adjust for risk I look at things like dividend growth track record, debt vs equity, safety ratings from value line, dividend payout ratio, interest coverage ratio, sector, economic franchise (some people call this a "moat"), ROIC/ROE etc. I also like to see how a company fared in the last few recessions (revenue, earnings, interest coverage, cash flow , dividend etc.). After a stock passes through my safety filters I then filter for a minimum dividend yield, growth level and discount to fair value. It's an extremely discriminatory process that, at this moment, filters out all but 5 stocks on the US stock exchanges.
You are right that exponential growth cannot continue indefinitely. Bacteria can grow exponentially and over short durations but fortunately the growth always hits a wall before they take over the universe.
That said a 7 or 8% rate of compounding isn't nearly the same magnitude as something like bacteria doubling every hour. Coca-Cola won't take over the market growing at 7 or 8%, however their growth will likely slow down the bigger they get.
It would be nice to "beat the market" but I see that as a fools errand (or perhaps an investing geniuses errand but most people who try to beat the market fail). I would prefer to just collect a rising stream of dividends from fantastic companies that are almost sure to raise the dividend year after year due to well run businesses with sustainable competitive advantages. I believe in diversification because odds are I will be wrong in some of my stock choices in spite of all my research.
I am also an indexer, John Bogle provided a great gift to civilization with Vanguards low fee broad based index securities which I use. I also follow an indexing strategy using target date funds in my employer matching pension program. So I am DCAing into an index fund every month, I have my wife's work pension set up the same way.
I looked up St. Petersburg paradox and I have no special competence that would allow me to discuss anything in regards to that.