Yes, the majority of breakout chains/startups are started as chains/startups.
But, plenty of breakout businesses aren't built to scale out fast. Starbucks didn't break out for over a decade. Microsoft didn't get the DOS contract until '81.
Meanwhile, lots of small businesses are small deliberately. Thomas Keller isn't franchising Per Se. Grant Achatz isn't franchising Alinea.
So what does it tell us when a company runs a single restaurant for 10 years, or refuses to take VC funding or hire ahead of revenue?
Exactly nothing.
Alinea was funded by 8 futures traders who each put in half a million dollars.
From the site:
Opened in May 2005, Mr. Kokonas says Alinea grossed $3.5 million its first year, an average of $14,000 for every night it was open. There are eight investors: The smallest stake was $75,000, the largest Mr. Kokonas', at just less than $500,000. Return on investment is expected to exceed 20% per year, he says.
This doesn't sound like an old-school arts patronage to me.
(edit: typo)
You have to already be famous to start one, you have to have met a rich guy who thinks investing in you will make him cool, you only cater to a class of people who in previous centuries would be known as "the aristocracy." Etc.