It doesn't generally fall to women where there are two parents involved - it initially falls to the parent who completes the application so that single parents (who are mostly women, but by no means all) cannot be discriminated against for being single. If two contacts can be added, that means that only having one entered implies that there isn't a second with all the prejudice that entails.
It's for the most basic part of the process - the bit that boils down to the name, address, date of birth of the child and a single point of contact. As soon as an offer has been made and accepted, plenty then don't just notify a second parent (and preferably a third contact for emergencies), they switch the priority.
To have double the contacts doubles the amount of emails generated, which has a massive effect upon the mailing system - over a certain number of emails sent, organisations either experience throttling of the system or have to pay for additional capacity. It increases the likelihood of the emails being erroneously identified as spam by internet service providers, meaning nobody using Outlook/Yahoo/whatever receives emails. Sending out that many can and does overload the exchange servers, meaning that people don't receive their emails - these are why different areas get their outcome emails at different times of the day on National Offer Day; the volume is such that even with just one parent contact at that point, it's impossible to send them all at once, especially when there will also be people logging in and using the app servers, contacting the local authority by email, phone and at times in person, and is why outages are not unusual on the day.
It then has a knock-on effect upon school messaging apps for the same reasons. Somebody has to go into every single record (once they are imported) to check addresses, check priority, tick as having parental responsibility (and this is assuming that nobody has ticked it when they don't have it). They have to manually enter a second address and that they also wish to receive correspondence.
There's double the data to upload to the payment system. Double the letters to generate. Double (if not more) the numbers of people to support in entering their user name and activation code. Increased costs because the payment system suppliers will encounter the server and bandwidth/sending demands. It takes longer to export double the data.
Then there's twice the paper (as there are always people who won't activate accounts). Twice the number of questions about term dates and uniform lists and start times and class choices because they haven't noticed they've already been sent them by email or it hasn't been received. Double the number of 'I can't find my login/forgot my password/what does this email mean'.
Every electronic act has a cost in human time and in environmental impact - doubling the demands by starting from a point of two people always contacted for everything doubles the costs.
Oh, and if you are considering a joint email address for one parent's record, make sure there are two separate email accounts as well - because once one provider fails to whitelist the school/local authority contacts as bulk emailing but not spam or if somebody loses their password, accidentally (or deliberately) blocks it or otherwise is unable to access it or recover the account, the school will need a second to deal with the inevitable bouncebacks and resend items manually.