There are non-metaphysical treatments of causality. I'm not sure if any particular interpretations are favoured around here, but they build on Bayes and they work. (I have yet to read it, but I've heard good things about Judea Pearl's Causality.)
It's a "psychological projection" inasmuch as probability itself is, but as with probability, that doesn't mean it's never a useful concept, as long as it's understood in the correct light.
Sure. But,
The way I see causal language being used doesn't suggest to me a demystified understanding of causality.
Maybe I'm being dense but it seems to me a non-metaphysical account of causality won't a priori exclude backwards causation and causality loops. In other words, even if we allow some kind of deflated causality that won't mean Newcomb's problem "makes no sense".
One day, you and the presumptuous philosopher are walking along, arguing about the size of the universe, when suddenly Omega jumps out from behind a bush and knocks you both out with a crowbar. While you're unconscious, she builds two hotels, one with a million rooms, and one with just one room. Then she makes a million copies of both of you, sticks them all in rooms, and destroys the originals.
You wake up in a hotel room, in bed with the presumptuous philosopher, with a note on the table from Omega, explaining what she's done.
"Which hotel are we in, I wonder?" you ask.
"The big one, obviously" says the presumptuous philosopher. "Because of anthropic reasoning and all that. Million to one odds."
"Rubbish!" you scream. "Rubbish and poppycock! We're just as likely to be in any hotel omega builds, regardless of the number of observers in that hotel."
"Unless there are no observers, I assume you mean" says the presumptuous philosopher.
"Right, that's a special case where the number of observers in the hotel matters. But except for that it's totally irrelevant!"
"In that case," says the presumptuous philosopher, "I'll make a deal with you. We'll go outside and check, and if we're at the small hotel I'll give you ten bucks. If we're at the big hotel, I'll just smile smugly."
"Hah!" you say. "You just lost an expected five bucks, sucker!"
You run out of the room to find yourself in a huge, ten thousand story attrium, filled with throngs of yourselves and smug looking presumptuous philosophers.