I know that a canonisation (in these days where the Pope declares saints) is actually considered to be an infallible act. To disagree with the declaration of any saint would be sinful.
What process is gone through in regard to Doctors of the Church? I imagine it’d be almost as rigorous, since one of the requirements is a life of eminent sanctity, and thus quite possibly the declaration of a Doctor is an infallible declaration too. So you could possibly be rejecting infallible teaching by rejecting the women Doctors of the Church.
As for their own feelings - most of the Doctors were equally humble and would’ve been equally uncomfortable with public recognition. Aquinas himself said towards the end of his life that everything he had written was straw. It isn’t relevant in regard to their fitness for such a status.
As for these female saints not having teaching authority or authority over men - St Teresa was spiritual director to numerous men, including at least one of her own brothers, for starters. And her writings, for the most part, were designed for instruction. No-one in the Church seems to have had any problems with either role (spiritual direction of men or catechetical writing) for her.
If no-one criticised her having this sort of authority or doing this sort of teaching during her life, then surely her being a Doctor of the Church is not an insurmountable step