I fully agree that the recruitment process needs to be monitored to ensure that no candidates are discriminated against on the basis of protected characteristics.
I don't believe that the role should be marketed to people from a certain background, instead, I think that any marketing of the role should simply discuss what the training and the role are like on a day-to-day basis.
The male brain and female brain work differently, that's no doubt a key reason why we see loads of female primary school teachers, yet more male pilots and engineers. Some would say that society conditions people to think in certain ways (i.e. men as pilots and women as cabin crew) however, if people really want the job in question, I think they'll overcome this conditioning.
Surely if the airlines offered training programmes like typical apprenticeships where you pay nothing for your training and are paid a salary, the diversity of applicants will be massively increased. I went through the train driving mandatory assessment process (which I passed) and the diversity of applicants was huge, no doubt because they didn't have to worry about funding.