This is part of why JSX has always been function calls rather than a data structure to interpret: the recursion to walk the tree is flattened at "compile time".
I don't see why it is a problem you'd need to import your `jsx` function in every file that uses JSX syntax, but perhaps because that's how I've always preferred to use JSX, even with React. Explicit imports are better than implicit ones. If you use lit-html you have to import its `html` function everywhere to get html`` template literals to work. It's not a lot of overhead and it works well. You can add the auto-import smarts to your editor, to your snippet files and template files. Typescript already has a ton of auto-import suggestions as you write a file.
Still, I don't like the React-classic style, the React-autoimport style, or the hybrid that you're advocating for. None work be very ergonomic and require tooling to at least give you errors that you forgot an import, which defeats the purpose of standardizing it at that point.