First of all, why bother doing that? Well, I think that it helps drives a few points home. It shows us the disparity between Qui-Gon’s ethics and those of the Jedi Council, instead of simply having Obi-Wan tell it to us later on Coruscant. It makes it clear that (in Mrebo’s words) “she is left behind because the Jedi don’t make allowances for parents tagging along,” but also that Qui-Gon is the kind of person who would free her anyway, while still understanding the difficult position it puts them in. All of this supports the thematic idea that Qui-Gon would have been the right person to train Anakin successfully, because he isn’t as dogmatic and black-and-white-morals minded as the Jedi Council. Anakin needed understanding and flexibility, which the Jedi didn’t offer - but Qui-Gon certainly seemed like he would have done.
It also means that Anakin’s frustrations with the Jedi arbitrarily forbidding him from seeing his mother in AOTC serves to highlight the whole “Qui-Gon and his lackadaisical approach to the Jedi Code was the right way to do things” idea, by absolving Qui-Gon of being (in retrospect) a complicit arm of the Jedi Council when it comes to Shmi, and Anakin’s attachment to her.
These are really good points!