At first I could see the repulsion to this, but if you think about it a little more, it's not a whole lot different from ordering a "white pizza" which is essentially using a bunch of garlic infused olive oil in place of the tomato sauce. Mayo is just oil emulsified with egg and an acid. I would definitely be willing to try something like this. In fact I've already had something very similar on many occasions.
There is a restaurant near me called Penn Station, which sells a fantastic Vegetarian option. It's sauteed artichokes and mushrooms that are placed on a crusty roll that's been smeared with Mayo. They then add a bunch of mozzarella cheese and some oregano and broil the whole thing until melted and golden. It is fantastic, and the mayo goes really well with the briny artichokes. It's a very filling sandwich. I'm not even vegetarian and I would order it sometimes instead of their signature cheese steak sandwiches.
