By the end of The Awakening by Kate Chopin, Edna makes some life-changing discoveries and has learned what to do to be free. She learns that she wants to be valued for more than being a good wife and a good mother, so she disengaged herself from those roles. She learns that spending time with people who had never been part of her social world gives her pleasure, so she spends time with them. She learns that, as a woman, the expectations society places on her are restrictive and unfair, so she flaunts them. She learns that she has a creative side, and she expresses that through her art. She discovers that sex can be pleasurable, so she tries it. She learns that she wants to be free of the restrictions placed on her by society, so she removes herself from it in order to be her freest self. She learns how unhappy she is, so she begins to pursue happiness.
This list of discoveries and actions should indicate a woman who was miserable but is now completely at peace and happy; unfortunately, that is not true of Edna Pontellier. She does have her moments in each of these areas, but she is unable to find the fulfillment and satisfaction for which she is looking. Each of them has a caveat which continues to leave her unfulfilled.
Though she does manage to free herself from simply being a wife and mother, Edna does not find complete satisfaction in that freedom. Though she meets many interesting people from many walks of life, they do not fulfill her and she eventually withdraws from their company. Though she recognizes society's inherent unfairness toward women and their roles, she continues to suffer because of them. Though she finds some solace in her art, it does not bring her satisfaction for long. Though she rediscovers sex, Edna does not love the man she is having it with. Though she removes herself from society, being alone just reminds her how much she longs to be with Robert. Though she does pursue happiness, she is not happy.
In the end, her realizations create in her a desire she sees no way to fulfill.
Despondency had come upon her there in the wakeful night, and had never lifted. There was no one thing in the world that she desired. There was no human being whom she wanted near her except Robert; and she even realized that the day would come when he, too, and the thought of him would melt out of her existence, leaving her alone. The children appeared before her like antagonists who had overcome her; who had overpowered and sought to drag her into the soul's slavery for the rest of her days. But she knew a way to elude them. She was not thinking of these things when she walked down to the beach.
Perhaps Edna would have been less discontent with her life if she had never learned that things could be different; however, once she knows it, she eventually becomes desperately discontent. Said another way, when she did not know she was a prisoner, her life seemed restrictive but not impossible; once she knows she is a prisoner and frees herself in part, her unfulfilled desire for total freedom causes her to despair.
Edna's decision to end her life, then, is based on her lack of hope that things will change and on her own inability to face things as they are: call it despair and cowardice. There is nothing brave about her actions. Imprudent does not seem to be a good choice, either. It seems to me, though she has her reasons, to be an act of cowardice because she knows how to swim, but she does not want to do it.