How is ID going to help with this in any way? They charge you (bank account/CC) and send you stuff (address), they inspect the return (or rather Should inspect it). What more would they need?
They don't inspect every return - that would make the already ropey economics of allowing returns very unviable - and it's often hard to detect return fraud because the fraudsters are returning an object that's nearly the same as the real thing, just used in ways that maybe aren't obvious given a casual inspection. Or they've raided it for parts and the object looks the same but the internals are gone.
It's not only Amazon that has this problem btw. Lots of online stores do. Return fraud is so prevalent that you should expect to this to become more common. A few bad apples ruin it for the rest of us.
Payment details aren't enough to reliably establish identity in many cases. If fighting this stuff were easy they'd have done it already, they aren't idiots.
So how is buyers ID going to help with Amazon not inspecting returns? Amazon doesnt even mark returns in any way so they dont know where it came from and where it ended up. Hell, they dont even mark/track source of co-mingled inventory!
And crucially - Amazon doesnt do this tracking on purpose so they can have plausible deniability while screwing merchants.
It doesn't help with inspecting returns. It simply adds another hurdle that has resulted in a slightly smaller percent of fewer returns, saving them a significant amount of $$ at scale.
Btw, if Amazon is a fault, where they can't shift the loss onto a seller or third-party, the delays will go on for weeks, if not forever. You have to do a chargeback.