I don't think the Lucases feel that Charlotte as a daughter, per se, is a burden but, I agree that, in a large family of small fortune, any child going off on their own has to lessen the financial burden a great deal. Also it frees up a space in the vehicles, in the home and frees up servant time to attend to her needs, etc. So from an economical standpoint, there must be a great sigh of relief because from that standpoint, Charlotte would be a burden for the rest of her life if she were never to establish her own household. I am not saying I agree with how she went about it, but these are things that must have been on her mind, particularly with young brothers already griping about having to support an old maid if it should come to that.
I do believe her though, when she says she has never been romantic.