Even if they could, we probably don't want the researchers paying for their results to be duplicated. This would create perverse incentives, similar to what happened with investment banks and credit rating agencies. If the original researchers must get their results confirmed in order to get published, and it is them who are paying for the confirmation, they will naturally tend to choose confirmatory labs that are more likely to confirm their findings. Since the labs would then rely on the researchers for funding, that would create pressure on the confirmatory labs to adapt their methodologies in ways that make it more likely that results get confirmed (even when the original study may not warrant it).
We want confirmatory labs to have no special interest in either confirming or disproving a particular study, but in improving the overall quality of research.
Since a journal's reputation depends (at least in part) on the quality of research it publishes, the journals would seem to be the natural candidates for the source of funding of confirmatory labs. Whether they'd actually be willing to do it another matter...