The "no seat" rule is just there to make the airlines happy because

It's a little more sophisticated than that.
Airline seat backs are not as rigid as auto seats. The problem with the
earlier safety seats was that they would not withstand a rear impact and
would fold in half, crushing the child.

I don't see how the design of the airline seat makes holding the child
in your lap easier. We're not talking about child seats in this part of
the thread, only why the FAA allows you to hold a child.

-Robert