You're comparing a situation where there's an unpaid family member, with a situation where the only person cooking is the information worker. In reality, there are a multitude of arrangement between those extremes, invalidating your argument.
Even then, health insurance costs differ between areas. Not to mention that the cost of every option you listed apart from using own time to cook is dependent on the local circumstances.
Similarly, travel and housing are very sensitive to geographic location, unless you want to travel across the world.
I don't think that "flawed economic thinking" follows from your second argument.
Who assumed that?
You're comparing a situation where there's an unpaid family member, with a situation where the only person cooking is the information worker. In reality, there are a multitude of arrangement between those extremes, invalidating your argument.
Even then, health insurance costs differ between areas. Not to mention that the cost of every option you listed apart from using own time to cook is dependent on the local circumstances.
Similarly, travel and housing are very sensitive to geographic location, unless you want to travel across the world.
I don't think that "flawed economic thinking" follows from your second argument.