Whilst I personally am lucky enough to be breast free, I don't think I would be fussy although I do understand where others are coming from.
A chaperone is necessary but this can be a health care assistant, it doesn't require the specialist training of a radiographer so would still save time and money if lack of trained personnel is currently causing delays.
A choice can be offered where possible, but as others have said, if something is found you will very quickly be being examined manually by a surgeon, the majority of which are male anyway.
I have often (but not always) found gynaecological examinations by males to be gentler and more considerate - sometimes female clinicians can be a bit rough if they personally have never experienced any kind of pain or trauma in that department and assume anyone finding it difficult is just being a little princess.
I did have a male midwife come to the house in 1998 after I had my first child. He didn't need to examine me, but told me it was particularly important to get my smear as teenage mums tended to be at higher risk of cervical cancer.
When I questioned the biological mechanism for this, he said it was because they are promiscuous!
I don't think that's a gender issue though, some people just aren't suited to a patient facing role
