My experience is the opposite, when people is unmotivated or not interested in the work, its unlikely for them to improve even if you give them enough chances.

I have the impression that people get in some kind of comfort zone when underperforming that's psychologically hard for them to improve until they move to another team/company.

So, you should catch these issues as soon as possible to let people know that this is not tolerated, in some way, this helps because people can take you more seriously.