You must have very good health professionals!
I take your point in obtaining medical reports in support of your claim, and sincerely hope that they will be useful in securing you entitlement to ESA, hopefully without a medical assessment in the process, but at the risk of throwing another spanner in the works, if you make it known to the ESA decision maker that you have obtained the letters of support "on your verbal request," there is a danger that the decision maker could decide that you "had put the words into the mouth" of the healthcare professionals, and these letters were not an independent assessment of your limitations based upon what these HCPs already knew about your medical conditions. Furthermore, if it came to light that letters had been amended at the request of the claimant, their validity would most certainly be called into question.
Decision makers are told that medical reports have to be factual, objective and wholly independent and if there is any suspicion aroused that they are not, they can be dismissed as evidence. Appeal tribunals are particularly wary when appellants have requested medical reports of their own volition, and can adjourn the hearing to confirm their authenticity if necessary, although this is uncommon because they will normally reach a decision on weighing up all the evidence, after hearing all the parties involved with the appeal.
When all is said and done however, I agree that ultimately it is up to the members to decide for themselves if they wish to request letters of support and/or medical evidence.
Nothing on this board constitutes legal advice - always consult a professional about specific problems 
