Thanks for your thoughts on this issue; I have a couple of millennials at our house.
My son is very connected to his phone, but also loves to wear watches (some of which have been passed from his father...) and is quite interested when something new appears on my wrist. He likes the divers and larger pieces.
My daughter is less interested in wearing a watch, but immediately grabbed my LE Mickey Mouse designed by Damien Hirst put out by Swatch. She is interested in the fashion side of it, but also will wear a watch with sentimental value.
I believe there will continue to be interest by people of all ages. The key will be finding the models/designs which appeal to those that will/can purchase. The Moonwatch has not gone out of style despite being around for 60+ years because the design continue to grab interest. Same with the fashion watches or those put out by Swatch. Time is a commodity that we all need to attend, and the number of ways to keep track will change over time, but I seriously doubt watches will fade away into obscurity.