If your belongings must be properly stowed during take off and landing and can't hold your purse on your lap, then why can you hold a child? Similar weight in some circumstaces.....
For me, the inconveniece of travellig through the airport with my car seats is minimal, compared with simply the comfort of having my children in a familiar seat and safely restrained.
Seems like there is no convincing one side of the other's viewpoint in this age old question. Now, onto children in business class/first...