In order to pass time, I am going to speculate about the role of greatsword in Mathilde's life.
There are many things a greatsword symbolizes - her blazon, the symbol of her order, one of the swords of the EETC - but one, I believe, was not mentioned. A greatsword (blade) is the badge of office of a Greatsword (trooper). And the in a sense, Mathilde considers herself the last Greatsword of Stirland and the only one who didn't fail her duty.
When she started training with the Greatswords, they accepted the adorable but deadly serious little girl as one of her own. They didn't reject her or make fun of her as she feared, but instead treated her as an equal. The Greatsword champion became something of a father figure to her, one of several, perhaps, but a father figure nevertheless. Perhaps the most caring one, given the personality of Regimand (her other, more significant, but also a more stern and sarcastic father figure) and the fact that Abelhelm was something different. Her greatsword is the very same greatsword Marcus gifted her and taught her how to use.
During that fateful battle at Drakenhoff, she was dealt not one, but two blows: Abelhelm died, and Marcus and the Greatswords failed their sacred duty of protecting their charge. The greatswords have but one true duty, and when it was necessary they were not their - all but one, the youngest and smallest Greatsword of Stirland. And despite doing her very best, she was not enough - and she couldn't forgive Marcus and Greatswords for that, their failure wounding her deeply because of their closeness. And neither they could forgive themselves, so they chose to go out in suicidal charges, joining the Slayers, and so Mathilde became the last Greatsword, and while she wields that blade the company still lives.
And that's not a good thing.
Stirland has a new countess-elector, and she has a new greatsword company - one raised in Altdorf and having no links to Mathilde's broken company. Abelhalf is dead and his Greatsword company no longer has a purpose and should be disbanded. Mathilde needs (and arguably has) to move to acceptance of his death, and in my opinion, her setting aside the particular flamberge she is wielding now would be the final symbolic gesture. Not cast aside, but hang respectfully in her living room. The Ablehelm's Greatswords have served their purpose and belong to history. In truth, I don't care if the weapon she replaces it with is a greatsword, greataxe, or something more exotic - I just believe that for the sake of her mental health she must set her current one aside and get a new one.
Well, that, or we should all join Omegahugger faction. Either works.