Contrary to popular knowledge, free market companies don't grow to take over the world. They grow until they get strangled by their own bureaucracy, and then rot away to be replaced by a younger, nimbler company without the bureaucracy.
History is full of examples. Just look at the top 10 American companies by market cap, decade by decade.
Sounds like an interesting exercise. Let's look at the ten largest American companies by market capitalization in 1960.
1. American Telephone & Telegraph is now called AT&T and was in the top 10 within the last decade.
2. General Motors has dropped off the top 100 for a while, but was the world's largest automaker within the last decade.
3. E.I. du Pont Nemours dropped off the top 100 in the last few years, but was the world's largest chemical company within the last decade before selling off Dow.
4. Standard Oil Co of NJ is essentially ExxonMobil and has been the #1 largest company within the last decade.
5. General Electric has been in the top 10 within the last decade.
6. IBM has been in the top 10 within the last decade.
7. Texas Company is now called Texaco and is part of Chevron, which has been in the top 10 within the last decade.
8. Union Carbide had one of the world's largest industrial disasters, and its later history is involved with duPont above as part of Dow.
9. Eastman Kodak ceased being relevant in the last 20 years.
10. Sears Roebuck & Company has collapsed, last being the largest retailer in the 1980s.
tl;dr: Of the top 10 in 1960, half have been in the top 10 within the last decade (including the former #1) and one has been #1 within the last decade.
I do plan to go back farther in time; I think it will also be interesting.
The claim about RCA seems unlikely. Radio Corporation of America stock grew very fast through the 1920s, peaking in September 1929 before the crash. However, even at the very end, it doesn't seem to even have been top 10 among industrials in the S&P index: http://piketty.pse.ens.fr/files/McGrattanPrescott2001.pdf#pa...
Instead, on that list we have companies like General Motors, General Electric, and Standard Oil of New Jersey that were still big in 1960 (and as mentioned above, some still so in the last decade).
History is full of examples. Just look at the top 10 American companies by market cap, decade by decade.