I would recommend Walter Mischel's 2014 book "The Marshmallow Test." He argues that the power of the marshmallow test is not in demonstrating that some children innately have more self-control than others, but in revealing how this skill can be cultivated and improved with practice and the right strategies.
I think the critiques are completely valid, Mischel did not account for many variables like socioeconomic status, family environment, etc. However, I do not believe it necessarily disproves his conclusion of being able to cultivate skills like self-control.