I suspect that, because doctors were historically always men, and may well still be in the majority, women are resigned to having to put up with male gynaecologists and breast surgeons, but as mammograms are always carried out by women, we haven't had to develop the same resignation.
As male mammogram techs would need to have a chaperone present, won't this end up making the service more expensive - as well as potentially putting off some women?
Also, I can't see how they would always be able to offer women the choice of having a male or female tech doing their mammogram - when I get mine, it's in a caravan in Morrison's carpark, and there is only one tech there - so a whole day's worth of mammograms are, I assume, done by the same tech. So they would have to have a whole day's worth of appointments all with a male tech. Presumably the appointment letter would have to say "When you come for your mammogram, it will be done by Geoff, our new, male tech. Please ring and cancel your appointment if you don't want a male technician squishing and manipulating your boobs (and hope we don't put you back to the bottom of the list as a consequence)". Then if only a handful of women are happy to have Geoff do their mammogram, the van will be standing idle for the rest of the day.
And what if, due to sickness, Geoff has to take over in Morrison's car park, and I walk in expecting a female mammogram tech, and find Geoff there - I am sure many women would find that a bit unsettling - I certainly would - but might feel they had no choice but to accept Geoff's ministrations if they wanted to get their mammogram done.
Can anyone tell me, for a certainty, that men never choose gynaecology or breast surgery as their field of study, because they like the access it gives them to women's bodies? I doubt they can, and I don't see any reason why mammogram technician would be any different.