Why don't commercial airliners use variable sweep wings?
Variable geometry is not used in commercial aircraft design for the same reason that they initially became popular in the 1960s but have fallen out of favor in more recent times: any kind of aerodynamic performance gains associated with the design is not worth the additional weight increase, and subsequent decrease in payload, associated with variable sweep wings.

There have been attempts to do so in the past. The ill-fated Boeing 2707 SST was supposed to make use of swing wings but designers could not achieve their payload goals with the design.   Usually more judicious application of aerodynamic principles during initial design is far more advantageous then beginning to design out right with a swing wing.