I think the Predator gives a small sporting chance to his prey. He doesn't deliberately put himself at a severe disadvantage, but neither does he "perform the interplanetary equivalent of hunting a deer with a rocket launcher."
I mean, yes, he has a lot of technological advantages. He has his cloak. He has his shoulder cannon. And he's big and strong physically. But you'll notice that in the first movie, he's taking on, basically, the entire Colombian guerrilla army, Jim Hopper's Green Beret squad, and Dutch's rescue squad. That's a lot of firepower for one individual to take on. The Predator needs his technological advantage to survive against numbers.
Once it's down to just Dutch and the Predator, mano a mano, he drops his helmet and shoulder cannon. Yes, he's still got his wristblades, but it's not like Dutch couldn't find some tree branch or sharp stick in the jungle to use as well. It's not even, but it's about as practically even as the Predator could make it without getting goofy and bending over backwards like tying a blindfold around his eyes and one arm behind his back. It's still a sporting chance.
Yeah in the EU only the weakest predators use the laser gun and stealth. The best ones only fight with the wrist blade thing, for what it's worth.
I think a lot depends on the specific adversary. They're much more likely to fight with only melee weapons against the xenomorphs (Though they use acid blood-resistant weapons, which the AvP movie fucked up). Against humans with guns, it seems more likely to warrant use of the shoulder cannon, since they don't want to cede the range advantage.