Mental load of paying the bills (not sure if the OP knows how a direct debit works) can be offset by the mental.load of having to be the higher earner. Things like presents etc can easily be sorted by just not doing it...
Mental load is not just paying the bills - yeah, monthly bills can be set up by DD, but renewing car insurance, house insurance, mortgages etc, checking deals for energy providers, shopping meal planning, remembering that you're almost out of tin foil, cumin, flour or other random thing that wouldn't necessarily be on subscription or the shopping list every week. Where things are on subscription setting them up and then keeping an eye to make sure you don't end up with 10 bottles of spray bleach because you are not using it at the rate the subscription is coming in. Managing family finances, savings, ISAs, pensions.
Managing the house, arranging for repairs, windows to be washed, managing the dog walkers (and if they do as people have suggested in this thread - cleaners etc), not just initial arrangements, but remembering to pay on time, managing schedule changes etc
For the child and family remembering medical appointments, figuring out what to do if child is ill and can't go to nursery, managing family social lives, knowing what clothes the child is growing out of and buying new etc, remembering that nursery are out of the child's nappies or he needs a fresh set of spare clothes because he came home in his spares the other day and that he needs new wellies because he's outgrown them.
As the child gets older remembering what is needed for school each day, PE kits etc, topping up lunch money, school trips, assemblies, remembering that they have to take in recycling for junk modelling day, that they have football after school or a party to go to at the weekend, remembering to RSVP to party invites, buying and wrapping cards and presents for the party. Ensuring that they have enriching activities outside of school so planning things at home, outings or extracurricular activities. Managing relationships with other parents for play dates etc, remembering to reply to messages from them, or the school WhatsApp group.
As the child gets older still, the planning and requirements for teenagers gets even worse, with lifts to and from friends houses or town, increased activities, picking up and dropping off from work / college / train station or if her husband can do the physical lifts remembering and reminding people who is where and when.
Even if she refuses to buy presents and cards for his family, there are still the ones for her family and their child, the child's parties etc.
I do all of the mental load stuff in our house (apart from food shopping) as well as working full time (and being the main wage earner). I don't resent it as DH does all of the food shopping and cooking and most of the evening lifts for my teens, so for us it evens out.
But to say that the mental load is just paying a few bills is the most ridiculous thing ever.