Take an example. Let's say they make an attack like Ice Jolt an ice/electric attack. And you use it against a flying type pokemon. The 2x damage from ice + another 2x damage from electric, and add that with the stab bonus from a ice/electric Pokemon. even tho that flying pokemon would be a much higher level than the ice/electric one, it would take considerable damage from the Ice Jolt.
dual type attacks sounds really cool. But as for game mechanics, it would make the game less fun to play.