The U.S. Postal Service doesn’t make financial sense because it is fundamentally not a financial idea. Like other aspects of Constitutional U.S. governance, its purpose is to stitch a people together into a nation.
Your argument rests on a pretty narrow definition of "financial sense".
Like when you buy food you like instead of the cheapest calories, this can make financial sense, because you value the preferred food more than the additional cost.
At around $20 a household projected loss for 2027, you wouldn't have to try very hard to do better than dismissing discussion of the value it does or doesn't bring.
It's current function is to deliver garbage to me disguised as useful information. Almost all of it goes into the trash before I bring it inside.
It doesn't make financial sense because Congress has capped how much the garbage manufacturers have to pay.
Unwanted advertising is hardly a unique failing of the U.S. Postal System.