* Be a sponsor's mouthpiece. This works pretty well if you're OK with your news being nothing more than someone's PR department.
* Advertising. This, as you say, hinges entirely on tracking users.
* Subscriptions. Also hinges on tracking users.
In short, you're absolutely right! There could be a better way! I just don't know of any and can't think of any.
I'm 100% convinced this failure of imagination is just my personal failing, through. I'm very interested in knowing what this better way could be, and I'm sure the news industry would similarly be deeply curious. What do you have in mind that's practical, workable, reliable enough to build a business around, and in no way, shape, form, or manner involves tracking users?