The Gallagher family in Shameless is absolutely flawed, but they of course do have a lot of love for each other. Conflict has been a common theme between them all since the very beginning, but they often have been able to find ways to push through it. Thus, this has been able to make them a very fun family to follow, as it certainly has been able to provide a lot of realism. This is even the case still with the show being in its final season.
However, there were a lot of previous characters who could have been intriguing fits in the family. In some cases, they were previous partners who should have been around more, while others may have just been smaller characters who provided a lot of humor when around. The show certainly integrated Kev and V as a part of the family, but other characters could have been excellent as long-term members too. It could have provided a lot of intriguing storylines if the showrunners decided to go down this avenue a bit more.
Mikey
The friendship between Mikey and Frank was so strong. It was a shame that it was short-lived though, as Mikey purposely went back to prison to receive free medical care. Mikey needed to be a bigger part of the family.
Although Mikey was flawed, it would have been cool if he engaged with the other Gallaghers more. It was clear that he meant a lot to Frank and it would have been hilarious if he partook in crazy hijinks in their house.
Mandy
Mandy was the one who got away with Lip. It was hard seeing her leave the series, as she clearly cared about Lip more than anyone else. This was evidenced by her doing everything for him, even if it was not appreciated in the slightest.
Although Lip ended up having a baby with Tami, it could have been nice if they decided to make Mandy a bigger part of the Gallagher family. This did not come into fruition, but it certainly was warranted given how much Mandy loved Lip.
Jimmy
Jimmy was a part of the family during the beginning seasons of the show, but it quickly ended. This was disappointing, as his connection with Fiona was simply the strongest out of any of the other men she dated.
Given the fact that he also dedicated a lot of time to them, it was strange that his story took such a dark turn. However, his criminal activity made it inevitable. Had he opted to avoid that life and stuck to medical school, perhaps he and Fiona never would have broken up.
Sheila
Sheila could have been the motherly figure that the Gallagher kids needed. It would have put less pressure on Fiona if Sheila had stuck around longer, but alas, this just did not occur.
Sheila also was a good partner for Frank, even though he took advantage of her far too often. Her kind nature would have been a good change for the family, as they were not like that most of the time. It's a shame that she was not a bigger part of the family, even if she did get a happy ending with her character.
Professor Youens
Professor Youens was a good mentor for Lip while he was at school. His downfall with alcoholism was awful to see, as he was once a glimmer of hope for Lip and his future. The show should have avoided this storyline and gave him a more prominent role for the rest of the family.
The Gallaghers definitely would have benefitted from him being their mentor. His wisdom could have helped them all not only academically, but also with all aspects of life. It was a shame that the series made him a short-term character at the end of the day.
Tommy
For somebody who was in the series from the beginning, it's strange that Tommy did not have more interactions with the rest of the family. He mainly spent time with Frank at the bar but did show some interest in what was going on in Lip's life.
Tommy really deserved a bigger role within the Gallagher family, as he ultimately had seen them all grow up from afar. Also, he seemed to be a better person than Frank, so he could have provided advice and help the younger Gallaghers especially.
Amanda
Amanda was a short-lived girlfriend of Lip's. She had her flaws, sure, but she could have been given a more prominent role with the family. She came from a wealthy family, so it was hard for her to relate to the others, but she did care about Lip deeply.
Amanda was another girl of Lip's who he treated rather poorly, but she did not deserve it. She was pretty good to Lip for the most part, so it could have been nice if they gave her more scenes with the Gallagher family.
Derek
Derek was Franny's father, so he absolutely needed to be more present with the Gallagher family. Debbie may have forced the pregnancy when she purposely stopped taking her pills, but Derek outright refused to help with the baby at all.
Derek ultimately should have been a bigger part of Franny's life. He had every right to be upset with Debbie over how this situation occurred, but he should have at least been there for the baby. Overall, this was just a mess of a storyline from the series at the end of the day.
Mike
Fiona and Mike had the potential to be a good relationship, but that just did not happen. Fiona infamously hooked up with Mike's brother, Robbie, which led to the completion of their relationship.
Mike was the person who could have gave Fiona a good and steady life. That would have meshed with the entire Gallagher family because they needed it badly. Alas, this did not end up occurring, as Fiona royally messed up one of the best opportunities for her.
Karen
Karen was a flawed character, as she of course was rather abusive towards Lip. However, she did become very close with him and should have been given the chance to have a larger role within the entire family.
Karen was Lip's first love and at the house often, but did not spend a lot of time with the rest of the family. It was a shame that her character ended up having such a tragic end due to the Mandy, as her being around more had the chance of providing a lot of cool storylines for the series.