For employees: salary/responsibility growth, bigger impact more quickly
You might be right about the customer side, that non-"startups" are more likely to be around in 5-10 years, which makes a difference when investing in a new, mission-critical area of your business (e.g. replacing email server)
Oh, but most startups are not trying to become big corporations. They're trying to be bought by one. This is the "get rich" part of the startup get-rich-quick scheme. Which is even worse for customers, because you can at least somewhat trust that a successful wannabe-big-corp will at least try to still sell/maintain their original product for a while.
It would seem this definition paints a startup as a proto-bigcorp. If the prevalence of big corporations is not a cycle we want to repeat, would we not favor businesses that do not intend to become big corporations?