I agree with you in theory, I often wonder however, whether many people experience what I would call spirituality and have not defined it as such. Also, how do we know what someone has experienced?
It seems to me that there is a centre/heart to every human being that I have come across. This heart is composed of love, and fuels such experiences as compassion, true giving, forgiveness, a wish to understand and not to change another etc. (see Paul's letter to Corinthians). Also this heart expects love and longs for love and understanding. Disappointment and hurt in not receiving it, in not being omnipotent and safe is also the driving force behind much disturbed behaviour. This seems to me to be the root of self in all of us, and gets buried by all the stuff that life brings. Therapy certainly is able to uncover the loving heart in a person. Is this spirituality however? I have not mentioned God. This work can be done without any mention or concept of spirituality, by someone who has opened their heart to themself.
I still have a difficulty with agreeing that someone not open to their spirituality should not be a therapist. Who is to judge? What are the criteria? etc. I prefer to bring the word love into the debate, and keep things simple.