It is clearly not a perfect system, and it does raise all the questions you have mentioned, so I am not going to defend it particularly vigorously, but here is a random array of thoughts...
AFAICT what this system appears to allow for is an open and honest process of outright negotiation around how the household works.
I cannot see a downside for that, and have seen (and practiced on many occasions) much more negative approaches - arguing, resentment, grudging, self-martrydom and so on.
If you and your partner are both completely spent at the end of the day then you can negotiate the remaining work, neglect it, or have one person accept it.
All of those are reasonable options at different times, what is important is not the individual decision, but the overall pattern and the process of communication and negotiation you use to get there.
To the kids it probably looks like mum and dad are negotiating over who gets to put them to bed. Ive (sadly) had my kids listen through arguments around that at times, and many other things, and overall they appear to have survived and even done pretty well, although they are still young so who knows.
I think it is fantastically easy for someone outside a relationship to look at it and go "that relationship is broken, there is no way it can work", and be completely wrong (or right).
Relationships tend to be pretty unique things. Maybe theirs is in good shape, and maybe it is not, but in general I dont see a problem with any process that helps them negotiate openly and honestly about what they want.
It is also fantastically easy to speculate on how badly kids will be damaged by behavior you personally dont agree with.
If you scrape the surface of why they are together and what their motivations are, I doubt it is the money. The money merely provides a proxy for them to build discussions around.
....or maybe their relationship really is based on money, who knows....