Yes, definitely. But I also think Townsend can be a good player on the left wing, given the fact that his right foot isn't that bad (I think his first England goal he shoot with the right foot) and his crosses are quite good aswell, better than Lennons imo. I think his player type is quite comparable to Bale, but Bale knew how to use his ability on the left wing, while Townsend doesn't seem to know it. So it's one more time a mental problem if you ask me.
You're correct that it was his right foot, but he wasn't far from dead center after cutting in from the right and moving past his man to shoot on his right. He is very ambidextrous, and this is part of the rationale for why I think he's a very useful player and should be kept. But he's recently molded the type of shots he likes to take cutting in from the left to the ones he likes to take cutting in from the right, and they simply don't go anywhere close to goal. If you've seen any old tape of him playing as a traditional left winger, you'll note that he never even attempted those kinds of shots in the past. It's as if his relative success on the right has made him even worse on the left because it changed his manner of play so much.
So maybe a coach would be able to drag it out of him, but until then I think it's far more preferable that he push Lamela for time on the right. With both those players healthy and under a good player-coach, that's about as good of a RW tandem as it gets in the league.