Why doesn't the Church speak more about exorcism and have exorcists speak out more about possession?

Major exorcism is a matter of supreme discretion and confidentiality. The identity of the diocesan exorcist is not generally made known, except to those who need to know. 
 
While procedures in dioceses vary a bit, it is most common that the exorcist works with a team that includes at least one other priest, a medical doctor, and a properly trained psychotherapist who all assist in the assessment of whether a person is actually possessed. 
 
If major exorcism is considered advisable, the exorcist proceeds with it, but only with the explicit approval of the bishop, who must concur with the judgment to go ahead with the major exorcism. 
 
Here too, the exorcist should never work alone, but with at least one other assisting priest and an appropriate team. It is almost never the case that exorcism is a “one and you’re done scenario.” Generally exorcisms are conducted over a series of sessions, sometimes weeks or months apart. 
 
If one suspects demonic possession, the first place to begin inquiry is always with the parish priest, or another trusted priest. If that priest has reason to suspect possession (rather than obsession or torment) then he should contact the Diocese and request consultation with the appointed exorcist.