I don't read all texts. I don't feel an obligation to respond to them either. Like phones - just because it rings does not mean I have to answer.
But I seem to be not the mainstream when writing to the therapist - if I write the woman - it is not to get a response (she does not respond well in person, I have no faith the woman could respond appropriately in a text or email) but more to get something away from me. The times I have forgotten and not told her not to respond, her responses have been useless - now, if I write, I am much more careful to instruct her not to respond.