Surely MN simply can't afford this? If the only advertising associated with it is for MN itself, the return on investment wouldn't add up. A few (or even a lot) of extra page clicks in return for a lot of real world costs?
You might suggest a partnership with the Royal College of Midwives or similar, if they had budget to do a patient information campaign. MN could supply some good, relevant and accessible content, but not the costs of the campaign.
And, yes, I think the Bounty angle makes this more complicated. MN does not want to look as if its campaign is commercially motivated, that would undo the great work so far.