The above paper gives a more nuanced explanation that the success of mental control depends on the lack of simultaneous cognitive load, which seems to fit what you’re saying.
But there also seem to be quite a lot of papers in which people asked to suppress are compared to controls with the result that suppressors fail and even experience a rebound after they stop trying. For example:
Wegner, D. M., D. J. Schneider, S. R. Carter, and T. L. White. 1987. “Paradoxical Effects of Thought Suppression.” Journal of Personality and Social Psychology 53: 5–13.
Wegner, D. M. 1994. Ironic processes of mental control. Psychological Review 101:34-52.
The above paper gives a more nuanced explanation that the success of mental control depends on the lack of simultaneous cognitive load, which seems to fit what you’re saying.
But there also seem to be quite a lot of papers in which people asked to suppress are compared to controls with the result that suppressors fail and even experience a rebound after they stop trying. For example:
Wegner, D. M., D. J. Schneider, S. R. Carter, and T. L. White. 1987. “Paradoxical Effects of Thought Suppression.” Journal of Personality and Social Psychology 53: 5–13.
Lavy, E. H., and M. A. Van den Hout. 1990. “Thought Suppression Induces Intrusion.” Behavioural and Cognitive Psychotherapy 18: 251–58.
Marcks, B. A., and D. W. Woods. 2005. “A comparison of thought suppression to an acceptance-based technique in the management of personal intrusive thoughts: A controlled evaluation.” Behaviour Research and Therapy 43:433-445.
And there’s even a book summarizing the literature:
Rassin, E. 2005. Thought Supression. Oxford, UK: Elsevier.