Meta-origins do not prevent that, but it does point to random OR not random. Mutants would logically be pretty random. Anyone who picked up an alien device -- presuming it was scattered about freely, if it's found only in the wilds of the Rockies going to filter people. But it would preclude its going to designated characters who know it's special for them.
If they were literally handed it, that would mean they had a task. Doubts and worries about their ability, or about the intentions of those who gave it. Even getting it from a Trickster means his random notions rule. Being the victim -- or willing subject -- of a mad scientist's experiments might mean nothing more than being where he could abduct you, but he still had his choices there. But, on the other hand, it's a lot harder to clobber some guy with it and have him have to cope. (Though some of them could leave random bits about that someone could accidentally pick up, it would require careful development.)
Taking out the meta-origin, or have several, would change things, of course.