" there's something inherently wrong with asking a woman (however much of an Amazon she may be) to do this."
that is a judgement YOU are making without asking the lady (or ladies) if they agree
I'd give you credit and say you were being gallant but some of the ladies would definitely say you were being sexist, misogynist and patronising
Placing the female sex on a pedestal is very Victorian but the world has moved on - they are capable of making up their own minds and deciding what they want to do - this is the 21st Century not the 19th.....