We should indeed make it clearer that we mustn't create an infinite loop (even though I hope every implementation already does this correctly - eclair does). I'm nitpicking, but with the change you're proposing, if we strictly follow the spec without thinking, we'd still be sending one redundant announcement_signatures:

• Both nodes send announcement_signatures on reconnection because of the requirement above ("If it has NOT previously received (...): MUST sent its own announcement_signatures message.)
• When receiving the remote announcement_signatures, they would respond with their own announcement_signatures, even though they already sent it right before
• Then they would stop re-sending announcement_signatures

It would be slightly more correct to change the spec to say that you only respond with your own announcement_signatures if you haven't already sent it since reconnecting:

- If it receives `announcement_signatures` for the funding transaction:
  - If it has not already sent its own `announcement_signatures` since reconnecting:
    - MUST respond with its own `announcement_signatures`.

Also note that all of this will be cleaned up with taproot, where we will need nonces to be able to create our own announcement_signatures, and will thus only re-send it after exchanging channel_ready (which will contain those nonces). We won't be able to have a loop of announcement_signatures message because we won't have nonces to create the partial signatures!

@ddustin ping?