I think you’re right. The best guarantee would be not to depend too much from any single source (ads, subsidies, private investment, etc).
A democracy has a vested interest in keeping independent newspapers afloat. Subsidies are not shocking, provided that this is impartial ans according to well-defined criteria, and that it does not become the main source of income for the media.
France has the Canard Enchaîné, which is thriving and funded only by sales and subscriptions, although it is well integrated in the political landscape. There are other examples in other countries but far too few.
But then the rest of your message seems to contradict that statement.
If "healthy and diverse press" is only guaranteed by single source of funding (state) then I don't see how this is diverse or healthy or independent.