In principle, you could make this work over something like video chat, but in practice I just don't see that working.
> We always knew that people bought this wine for fun.
> The buying process, and talking to others about the wine,
> turns out to be part of that fun.
So yes, you can strip out all of the fun bits and come up with a very efficient transaction process, it's just that the customers want the fun bits more.While we are getting better at recommendations, the best salespeople still have a better understanding of what makes you like a product than "people like you also purchased..." algorithms. This may be particularly important in markets that are about different things for different consumers: wine selection may be about taste, or it may be about social signaling. Same is true in the transaction: it may be about the best price, building a relationship, having a relaxing escape (buying cigars, for instance), or any number of other things.
I'm sure Amazon's algorithms often do have a better idea of what I'd enjoy than many of my friends, but friends' recommendations are still more likely to induce me to act than a personalised promo email.