Customer channels and user experience

In many of the places I work there is the concept of a customer access channel. That is - an interface by which a customer is able to interact with the business. For example - face to face in store, on the phone to a call centre, online web-page etc.
These have been extended to multi-channel and even omni-channel strategies where customers get similar or complementary experiences through all different mechanisms.
The idea being, of course Customer Focus (with capitals) and all the good things that come with it.

The trouble is that the entire focus is still on a discrete set of closely controlled access points. Most of which are conceived and built around a particular technology. But if we decompose this viewpoint you can see that there are overlaps in the technologies available - and generally they relate to the capabilities that may be offered, whatever the technology.
Hence - assisted channels, that is phone or store-front where you talk to a real person, have an experienced (sort of) user in front of the technology, and this allows for a much more complex (richer) customer experience. At the other end of the scale is voice systems talking to a machine, however well programmed, is restricted to a single set of menus and very simple operations. The overlap comes into things like using cash - which is restricted to store-front or self-serve kiosk (e.g. an ATM). Even through web channels the user experience on a smart-phone is different to a tablet is different to a laptop is different to a desktop - although many web-sites don't make the distinction.
The security profiles for mobile access, using the device id, cannot be used with a standard computer - especially through a corporate firewall.
A better way of thinking about the customer experience is thus by consideration of the set of capabilities that the access path offers - not by the 'channel', a concept which is becoming less and less well defined.