I agree with the general caution about buying a property and the baggage it comes with. Unfortunately with kids there be dragons in renting as well: having to move when getting priced out.
(This is sarcasm, of course, although I suspect the author is serious about avoiding things that many people find meaningful.)
And the cost of moving with kids is much greater than moving alone or as a couple. You will need to find new schools, activities, etc. It constrains your search space and will inevitably take a toll on your time budget.
The areas with decent schools etc also tend to be more expensive. When you buy property in such an area you can at least lock in a flat rate on your rent for the next 10-20 years or so, until your kids have grown up and can leave the nest.
So it does make a lot of sense to buy when you have kids. Either way, those "risky career moves" are anyhow much less of a good idea when you need to provide for a family.
Even as a couple it can be a challenge to move because of your career — it's rare that both partners get a career bump out of a joint move.
Houses have sizes, locations and whole spectrum of varieties that can be taken into account!