Loads don't fit that description. If there aren't a lot of traditional wingers of requisite quality, then maybe we should scout more thoroughly, or maybe we shouldn't insist on playing with 'wingers'; and switch back to a 4-3-3, where they will be more inside forward types and closer to the goal. If you have to buy certain players who are excelling in central roles, especially for massive prices, why shift them out wide and ask them to do things that will detract from their goal-scoring threat (which has become arguably Griezmann's biggest quality)? His best performances have come as a secondary striker or a #10. He has developed in to a world class player in Madrid in those positions, why sign a world class player and use his in a position that isn't his ideal fit?
Ref. above. He was as much of a winger for Real in his last season (which is when he started shining) as Neymar is for Barcelona, or David Villa was in the past. They played a base 4-3-3 with Griezmann tucking in and having the license to go centrally, which will again bring up the same conundrum of lack of width at United. He has become a world class player as a #10, or secondary striker under Simeone. If you don't want to believe me ask someone like kouroux, or the regular La Liga watchers. Ask them how good he will be as a classic winger, as opposed to a #10/ support striker/ inside forward; and playing just behind or off Martial in the left or right channels.
Juan Mata played wide for all three of Valencia, Spain and Chelsea, moreso the former two. Griezmann is a bit faster but playing wide for Atletico in some games here and there doesn't detract from the fact that he is most effective centrally. It's like buying Aymeric Laporte and using him as a left-back because he played there for Athletic Club a few times. Use players in their best positions, instead of toying around.