I think this is broadly true, but there are niche areas, such as frequent flier miles, where extrinsic motivation works for brand loyalty. Several years ago (before 9/11) United did a really terrible job of managing customer expectations during a job slowdown by pilots. I really, really hated United during that time. I probably would never have flown them again if I didn't already have over 200k miles on my account.
"There are niche areas, such as frequent flier miles, where extrinsic motivation works for brand loyalty"
While I agree with what you're saying, I think this is a bad example because frequent flier miles work more as a barrier to switching, rather than a classical extrinsic motivator. (You overpay every time you buy a ticket, and you don't get your money back if you switch airlines.)
I wonder if it works for customers, but not for employees?
Where broadly "customer" is "you're trying to persuade them to [X]", and "employee" is defined as "additionally, you're in a position of power over them".