For `touch a b; echo "$(echo "$(echo "$(ls)")")"`, I'll think about it.
It looks like a bad command to me (nested $ and nested `"` do not smell good). Probably I would mark this a wont-fix. But if I found I does make sense (useful in some meaningful places) - I'll consider to update cicada to align with Bash. Thanks for reporting.
Nested $() is fine, and not uncommon (though 3 levels like here is rarely used). All the nested "" present here are required, as removing any of them would cause a change in behavior (caused by word splitting).