Point #6 skims past what is (IMO) one of the most interesting results in Turing machine theory: adding additional tapes doesn't increase the computational power of the machine.
This is significant because machines at the next-lower level of complexity (pushdown automata) DO get more powerful: a PDA with two stacks is equivalent to a Turing machine!
Tangential: PDA aren’t really the “next-lower” model, just the one that we talk about most often; there’s a whole family of models that are stronger than a PDA but not Turing-complete (e.g. alternating pushdown automata).
This is significant because machines at the next-lower level of complexity (pushdown automata) DO get more powerful: a PDA with two stacks is equivalent to a Turing machine!