Our Gemara on this Amud discusses numerous circumstances of chalitzah must be chosen over Yibum. A fundamental question that has been discussed by poskim is if Chalitzah is it’s own Mitzvah, somehow a fulfillment of Yibum, or is it more comparable to the “Mitzvah” of Jewish divorce. That is to say, when one is in a situation that requires a dissolution of the marriage, it is a Mitzvah to perform it properly with a Get. In lomdishe terms is chalitzah just a matir, or is it a Mitzvah.
One practical halakhic outcome would be in regard to a person who has no need to perform chalitzah, and the woman also has no interest, would it still be wrong to hold off on chalitzah? This question was asked of the Chasam Sofer (EH II:85) regarding an elderly man whose brother died childless, and his brother’s wife who was elderly as well, and had no interest in remarrying. Neither wanted to go through the inconvenience and awkwardness of doing the chalitzah process. Do they have a right to refuse?
The Chasam Sofer says they do not have an obligation to do chalitzah. It is interesting because he does quote a Zohar (III:180a) which implies that chalitzah accomplishes something similar to Yibum, and the release of the shoe somehow also releases the dead brother’s soul to move on. Even so, he says that it is at best akin to saying Kaddish on behalf of the deceased. That is, it is a kindness to the soul but cannot be coerced by any external authority. He said it’s like lighting a yahrzheit lamp, which is indeed a good thing to do for the departed but not an obligation.
As an aside, the general tone of the responsum gives one the impression that the Chasam Sofer did not overly value the Kaddish or Yahrzheit ritual. He saw it as a kindness that one does, I suppose similar to kindness one might do for a living person. A good thing to do for sure, but not an obligation. In our times, Yahrzheit lamps and Kaddish are taken as obligatory customs, so perhaps we should behave similarly in regard to chalitzah.
Translations Courtesy of Sefaria, except when, sometimes, I disagree with the translation 
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