Millennials' Brand Loyalty isn't so Unique
I've always thought that the "Millennials aren't brand loyal" trope doesn't ring true. A brand is a cognitive shortcut. It is a means for a consumer to make purchase decisions on autopilot. The more distracted a person is, the less time they have to make informed decisions. Therefore, the more they have to rely on brands.
This research by eMarketer/InsiderIntelligence lends evidence to this point-of-view.
We can argue whether these unconscious purchases constitute "loyalty" or not. From my point of view a string of purchases constitutes behavioral loyalty. The question then becomes how enduring is that behavioral loyalty and under what circumstances can it be terminated? You can read more about my thoughts on that here: Amazon's Quintuple Threat to Brands (chaseintel.com)
The above reasoning may also help explain the relative price insensitivity of younger people.