The 31-year-old attacker spent the final year of his four-year stint in Celtic's first team as a left-back, with Strachan electing to play him there ahead of Mo Camara in a decision which never looked like paying off - and it never did.
Consequently, Wallace, now with Sheffield Wednesday, left Scotland without really fulfilling his potential, but it has been a different story down south.
The Scot left Celtic for Sunderland and has since carved out a very successful career for himself in the Championship, helping two clubs win promotion to the Premier League the decade since leaving Parkhead.
It was almost three promotions into England's top flight, but Sheffield Wednesday lost 1-0 to Hull City in the playoff final last Saturday.
But Wallace, who has just one Scotland cap to his name, feels a sense of unfinished business following a modest career up north, reflecting on the "strange reason" behind Strachan's left-back choice back in the day.
"When I was at Celtic I kept getting played at left back for some strange reason when that wasn't my natural position," he told the Glasgow Evening Times.
"People have made judgements on my career and my ability based on the fact that they still probably see me as a full-back. They have not seen me playing down in England every week.
"I have played a lot of games and I have had successful times in England. I have been promoted twice to the English Premier League with Sunderland and Burnley, I was one game away from being promoted again with Sheffield Wednesday, so I’ve had a fairly successful career down south.”
Wallace made some 35 Scottish Premiership appearances for the Glasgow giants.