Bitcoin's blockchain is described as a 'public ledger.' How does this public nature contribute to bitcoin's security and trustlessness, and what role do nodes play in this system?

Isn't public just another way of saying anyone can read it?

If anyone can read it, anyone can do math to verify it.

If anyone can verify it, anyone can be sure about the true state of the ledger without needing to trust anyone else.

If anyone can be sure about the state of the ledger, they can accept the coins anyone else gives them.

If anyone can accept coins, anyone can spend coins.

If anyone can spend coins, anyone can write to the ledger.

If anyone can do these things, anyone can run a node.