Just the fact that some photographers know they have a Leica in their hand, makes them feel more liberated and ... how shall I say it ... "photographery".
I think it cannot be denied that with a suitable picture style, you could shoot JPEGs on a 5D MkIII that look similar to what a Leica produces without processing. I bet you most people would be hard pressed to tell the difference between the JPEGs with their naked eye, and even fewer would be able to pick out which one was from the Leica, and which from the 5DMkIII.
Leicas remind me of French Wine. Everyone waxes poetic about them until they are asked to pick out the Leica photos from a lineup in a double blind test.
At that point everyone then says the Leica is about intangible things like "superior UI".
In the end, I think the Leica is a brand first, and then a camera with certain characteristics next.
A camera made from a solid carved piece of aluminum is just damn attractive. But people feel the need to imbue the Leica with more qualities than it actually has, because maybe they feel embarrassed to have chosen the tool of their trade based on its looks, rather than its utility.
I for one think designers should not apologize for choosing a camera just because it looks good. Design is their whole trade, and they need to surround themselves with inspiration to get into their creative space.
I look at Leica as the cost of doing business for a designer. That is the way their brains work.
And lest programmers develop some superiority complex about their rationality ... I want to suggest that the success of the Go programming language is about aesthetics at this point.