I've yet to meet a business leader who turns down customers who are "more valuable".
On the surface, we look at all of the channels in this image, and we think "if the customer touches more of them, then the customer must be more valuable."
Maybe.
Think, for a moment, about your relationship with your favorite restaurant.
I'll bet you have a favorite dish. At one restaurant, I have to order calamari ... can't help myself! And I'll cycle through main dishes, with two or three favorites, and others I'll enjoy on a whim. My relationship is with the restaurant. Each item on the menu is similar to a channel. Each time I visit the restaurant, the odds of me trying something different increase.
This is where we get the relationship wrong. A customer likes our brand. The customer manifests this gratitude via channels. We simply measure gratitude incorrectly.
Don't view channels as the end result. The customer likes you, and one of the symptoms of gratitude is use of multiple channels. You don't necessarily create gratitude by forcing the customer to use more channels.