I think it's more flexible than that.
If we're up against Klavan, a CB playing LB, you'd want Walcott to demand the ball often by creating angles to receive the ball. Stay wide, get it and run at that grock Kopite.
He did that. Once. In something like the 82nd minute. I remember it vividly because I was watching the game with an Arsenal fan from work who, in response to the venting of my spleen about why it had taken so long for him to realise he had the better of him, replied "that's Theo Walcott- fantastic on his day, invisible most."
Question- do you really think Allardyce said to Walcott- avoid running at Klavan? Even factoring in the instructions you say he had- to protect Coleman from Mane, are you suggesting he had zero opportunities to get involved in the game before the 82nd minute? I don't buy it.
There is no doubting Walcott's ability or his pedigree. He is and should be one of our best attackers. I just don't why we keep making excuses for him when he has quiet games. Especially given the masses who grab the pitch forks when Sigurdsson has a quiet game.