Maybe in a perfect world, customers would always have a direct line to their favorite member of a business' answering service, and that person would be the same one they could meet at a live location if something went wrong. But even an outsourced call center can create this kind of connection, and a well-run one will bridge the gap and lead to a growing relationship with the whole of your company and the various customers that interact with you.
Not to return to a tired old example, but Apple is exceedingly well-known for assertive employees and running a tight in-store crew. A recent Forbes article by Carmine Gallo looked at the radiating effects of this level of service by highlighting one local man, a doctor who bases his own strategy for good service off of the Apple method. This involves the basic arc of any interaction: greeting, listening responding, and departing on good terms.
When the customer and representative aren't standing in front of each other, these kinds of courtesies might be lost. And online customer services or text lines might feel especially awkward, at least at first, and especially with no video component.
However, if your representatives think of all of these different offerings as connected, as well as ways to drive customers in between them without feeling any sense of disconnect, they might help the consumers your business courts to feel more comfortable with you overall. It might not hurt to take a page or two from the businesses mentioned by Gallo, who openly take a page or two of their own from Apple.