What requires the format to be text-like?
I'm not sure I agree with this assertion. I think structural editors need to be language specific so that they can offer higher value edits that might only make sense for specific languages.
"Text-like" meaning easy to parse and universally understood. With language-specific (or indeed, all) AST/generic tree attributes serialized in a uniform way that does not entirely break parsing if an editor does not understand one of them. I.e. I can edit code even if my editor doesn't understand the language and doesn't give me syntax highlighting and completion. More, that that 'understanding' can be factored out of the editor core, as is done with language servers today.