Real important mail is usually in a plain white envelope, with first-class postage.
I would gladly pay $2 per stamp if it meant obliterating junk mail. Hell, charge me $5 a month just for the privilege of not receiving any. Just, somehow figure out what the true cost of delivering my mail is, and allow me to pay it instead of having to trash all the “subsidy” crap.
It shouldn't matter. Last 10 years or so, my cards had to be activated online first, before becoming useful.
Requires someone able to intercept the post (eg corrupt postal employee or subcontractor), and the ability to create a convincing replacement envelope/letter, but it is all achievable, and I expect not everyone will properly scrutinise the envelope/letter/card for signs of tampering. Even for me, with a new card only once every 3 years or so, how can I tell the difference between their letter being tampered with and them just using a new/slightly different design?
It may also be possible to pick the card up at the bank (instead of post delivery). I did that once before, too.
Doesn’t stop all crap, but certainly most, as the stuff sticking out my neighbours boxes without a “No ads” label proofs