The concern about a conversion therapy ban stems from witnessing how it has played out in other countries, Canada is a particularly concerning example. See image for acts which are now illegal in Canada.
The definition of conversion therapy in your link includes psychiatric and psychological intervention.
We know that a significant number of children referred to the Tavistock had a complex range of needs. IIRC 90% had comorbidities including neuro diversity (mostly autism), a history of childhood trauma (including sexual abuse), anxiety and depression and factors such a being bought up in the care system. Time To Think by Hannah Barnes covers this is detail using data from the Tavi. We also know from detransitioners that many feel they were not given enough time to explore issues around gender identity.
We also know that 85 - 90% of children will reconcile with their biological sex as they progress through puberty if a supportive watchful waiting rather than affirmative approach is taken. Many will reach the conclusion that they are same sex attracted.
Data from the Tavi also shows that 99% of minors prescribed puberty blockers will go on to take cross sex hormones.
I do not think anyone condones the abhorrent practice of conversion therapy but the evidence so far suggests that watchful waiting, for minors, and talking therapy may lead to fewer people making the wrong decision and undergoing irreversible medical treatment.
Please understand that this concern has nothing to do with persuading people they aren't trans but a desire to prevent children (and adults) being put on a medical pathway which can lead to infertility, sexual dysfunction and life long health problems.
Any conversion therapy ban must make room for talking therapy for anyone who is questioning their gender identity.