This article in the Atlantic talks about families using tools like Trello and Slack to keep track of each others activities and tasks.
It calls it treating the home like the office or running the household like a business and presents it like an oddity if not a 21st century abberation of family life. E.g. tracking how often you call your mom.

I find the tongue in cheek tone rather tone deaf. It misses the point on several levels.
The examples are not showing how families are run like an office or business. Families are seeing parallels between work and private processes.
After all task allocation and keeping track of each other is important in the household too. Besides households are the original economic unit.

Tracking tasks, also for children, has been around for ages. Dalton schools, with their focus on independent learning tasks, have had to do / doing / done boards since the 1920s.
Hallways and refrigerator doors have displayed lists and overviews forever too. My grandma kept track of everything in notebooks, how many beans harvested and stored for the winter, how much fuel used etc.
All it shows is that what families have been doing all along is also done using tools imagined for a work environment. Just like owning carpentry tools was once limited to masters who were members in a guild, and are now found in every household.

That is useful for several reasons. It helps make sure that the household and family get at least equal attention as areas of responsibility.
Keeping track of work but not the home easily means the home gets attention when all else is finished, which it never is.
For that reason I have areas in my GTD todo lists for me personally, family, daughter, partner and the house. Similarly I have long term goal descriptions for them too.

We would never have moved so quickly and readily early 2017 if we had not set it as a goal in the summer of 2013 to be ready by the end of 2016 for it.
It meant building up the financial buffer for it, and thinking about where we would want to live. As part of that we regularly temporarily moved to other cities for a month to figure out what we wanted.
Since July 2013 when we set the goal on the balcony of a friends home in Switzerland, I kept track of what we needed to do for it in my GTD tools.

It does sometimes feel odd to track things like how often I spoke to my parents. But it was necessary as my parents would often forget when we talked last. Sometimes telling me it had been weeks when it was yesterday.
So I made sure I called them at least once a week by having it in my todo lists. I also kept notes especially when their health deteriorated as they would tell my sisters different things, so we could compare.

For the household and for our family we have shared Evernote notebooks. To share receipts, info about daycare, holiday plans, or my itinerary when I travel for work.
Weekly we look ahead at what is happening the next week or two.

I mentioned the household being the original economic unit, and in one aspect it means I do treat it as a business.
Optimising household income also means I regularly spend time assisting Elmines business, as she does mine. It helps maintain and increase our freedom of action.
Every Euro I help her make and she me being better at what I do means improvement for us and providing our daughter with a good start in life.

If Slack or Trello, Evernote or Things help us do that then great.