Yeah, but no matter the why, Anne is not capable of living independently, and making adult decisions... Maybe in the beginning her plan was good, but now she has irreparably destroyed the Darcy's marriage - yeah the author will probably contrive a happy end, but I don't believe you can really come back from Darcy believing his wife to be @#$%& someone else and demanding his understanding of this situation. And Lizzie will probably not forgive him believing such rumors about her...
I don't know if an asylum is the best solution, or otherwise an estate in the country under the care of a relative where she can slowly learn to mature - but she had that at Rosings already... So maybe Lady C was not so wrong about her daughter... Maybe her illness is not so much physical but a mental deficit?