By removing Madge from the story of the original trilogy we also very much remove Maysilee and Merrilee set up - every time Katniss thinks of home out of the haze of confusion and denial that surrounds Gale/Peeta, Madge is on the list right next to her mother and Prim. Madge is very much one of the people that the capital interviews as Katniss’ ‘friends and family’ before or even after Gale himself. Madge gives her the mockingjay pin, from her aunt, in an act that is sentimental and purposeful - she knows that Maysilee was an original tribute with 12's sole victor of the time. Likely that Katniss’ mother and hers and her aunt were all friends as well. To send Katniss out with the token of a mockingjay is not only because it is something of a symbol of rebellion, because also it will very viscerally remind the people who will remember Maysilee that the hunger games needs to end. The generations of pain passed from mother to daughter and aunt to niece and sister to twin. Haymitch will remember, too, Maysilee at least as a tribute from his district.
Madge, along with Peeta, but more importantly Madge as the pinnacle of it all - serves to also represent the humanisation of the perceived ‘elite’ of the world of the districts. Her name is also in the reaping bowl, she will never have to draw extra slips, she will never starve because of her father’s and her family’s positions of power. But yet still, she dies. She is lost with district 12 and katniss can’t even register that she has lost Madge because of the sheer amount of people and concepts she has to mourn now. But it is so very stark – Madge is brought up every time Katniss thinks of the people she has to lose (hears her screams in the jabberjays of the Catching Fire arena, too) but Madge is not brought up much in Mockingjay so carefully. So purposefully that shows, to me, how Katniss can really never go back.