Many/Most dual line foils are cross bridled, that is a certain number of lines cross from right to left. The problem with simply bridling the right side to the right handle and left side to the left handle is you may simply pull down one side or the other and not really tilt the kite as needed to reduce pressure on one side and increase it on the other as needed for turning. Also most controllable foils are curved where the flowform has a flatter surface which won't trap pressure as well for turning.
Having said all that give it a try, theories are meant to be proved wrong as well as right