Is there anything wrong with this more symmetric aircraft design, and why isn't it used?
The biggest single problem with this is the location of the main spar - across the middle of the fuselage. This might not be a problem for single seat military or sports aircraft but would be a major headache for almost any other design. Imagine trying to load 100+ passengers with 50% of them having to clamber over or under a major obstruction in the cabin.

Yes, you can engineer around this but the resultant solution is likely to be heavier and more complex than simply moving the wing up or down and out of the way.