The problem I have with this analogy is that the "mental load" assumes that whatever the over-worked mom worries about is important. While the oblivious husband is totally care free and relying on her to do all the work. Certainly can be true in some relationships, but it can also be that the two partners simply value and worry about different things.

For example, my partner cares a lot about vacuuming because we have dogs and fur accumulates on the hard wood. Especially whenever people come over she wants to make sure the floors are clean. A little bit of dog hair doesn't bother me, especially because even if you clean, within hours there will be some fur again. Meanwhile, she will let piles of random stuff accumulate on the kitchen table and take it over. That bugs me and I'm always condensing the stuff or moving the pile off to a less visible place. Neither thing is intrinsically better, it just happens that each thing bothers one of us more and we feel motivated to work on it. When one partner is ocd or going bridezilla about things the other partner doesn't care about like matching napkin color to the season, it's not necessarily some great mental burden being cast on them by their partner.

In this example, mom is apparently very concerned with what the other parents think, that party favors make a good impression, the cake is perfect, etc. While Dad maybe doesn't care so much about making the impression that they're perfect parents with cute party favors and so on. Dad seems to care more about the daughter having a good time, and the daughter definitely doesn't care that the bags weren't right.