Ok so to make your postal service analogy accurate let’s add a detail: whenever you send a newspaper clipping the postal service opens the letter and inserts a piece of junkmail.
Ok now imagine the gov passes a law saying “if you insert junkmail into a letter containing a newspaper clipping, you have to pay a fee to the newspaper”.
Where’s the problem? Either they stop inserting ads, or they pay.
As for “make less money” vs “stop existing” - having journalism exist is in the publics interest. If one business threatens to cause another to go out of business we might not care, but in this case the business is theoretically socially important.