For the latter: if you delete your chat history, but your messages were incepted in flight, you want to ensure the keys that are still on your can't decrypt them.

Not sure about the first question.

In general it's better to stick to a well studied protocol than to make ad hoc adjustments to it.

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Definitely not my area but after a bit of reading it seems like this blog post does a really good job of explaining the pretty complex reasoning behind the double ratchet (used to be 'axolotl') setup:

https://signal.org/blog/advanced-ratcheting/

It seems like they're trying to address the difficulties of *asynchronous* messaging (users often offline for a while), as well as both forward and 'backwards' secrecy.