The programmers behind the Apollo missions were almost all female and between them solved many problems that came within a whisper of scuppering the whole enterprise.
A danger in the role swap plan is that once men get a greater foothold in childcare and all that goes with it, they would pin the whole patriarchy thing to it and it would suddenly become a high status, highly paid role. Women would become 'just engineers' :) We need to be alert to that sort of reversal.
Thanks for the shout out.