The question is how much of it should be automated that isn't already. It's not like they're building 737s and A321s for everyone - at some point, human labor just makes better business sense, though I admit I have no idea where those lines are - I don't have the factory experience to tell you.

It's also likely they'd pretty significantly redesign a lot of the parts if they were going for more automation - a lot of aircraft construction is done in a way that makes it difficult even for humans to get decent access - the robots to get into those kinds of tight spaces to work would look more appropriate on the International Space Station, and may not be much faster at the job due to all of the extra maneuvering to get in and out of tight spaces. (In fact, on most existing aircraft designs, to do much with robots you'd almost certainly need a human operator standing by just to make sure it didn't accidentally punch through a firewall or the tin can hull, since a lot of assembly steps require moving fixtures around and installing temporaries for support, which may be more ad-hoc than planned procedure.

As an example of design and construction philosophies, both Boeing and Airbus have adopted a more "outside-in" approach to building aircraft, where the principal components of the airframe are built first and everything is fastened to them as construction evolves. This is a very human- and aircraft-centric construction philosophy, since it means the workers need to move around the plane a lot, rather than the plane's components coming to the workers. This works better with the scales in mind, since the aircraft are already constructed in some of the largest buildings on the planet, and moving large assemblies around a lot during construction means employee downtime and slower delivery performance.

But what if instead they took a tunnel building-like approach where the interior would be mostly assembly-line built in ring sections, fastened together into modular inner compartments, and then fitted to external fuselage pieces before everything is snapped together in one big final assembly step? The smaller sections work better for both humans and automation, and the larger pieces snapping together Lego-like means you can even reduce the need for as many large assembly buildings down to just final assembly. It could possibly be much better for composite construction, as it would mean fewer external seams on the aircraft (which in turn must suck for the carbon fiber engineers, since it means even larger autoclaves and components they would have to deal with), which in turn gives you even more of the advantages you already are seeing on planes like the Dreamliner (plus likely a much quieter cabin, since it would be better separated and insulated from the hull, and fewer fasteners means less vibration noise generated as well as shorter assembly times).

Of course, Boeing and Airbus are huge companies with lots of extreme long term planning when it comes to budgeting and logistics, so I doubt if either company will make revolutionary strides in this direction rather than evolutionary strides. With product deliveries over multiple decades and lifecycles approaching a century, it's easy to see why these companies are conservative and evolutionary.