It’s true that you could get evidence from such an experiment which would allow you to update your posterior (although if you’re using significance testing like most experiments, you’re very unlikely to achieve statistical significance, and your experiment almost certainly won’t get published.) But even if you’re doing it purely for your own evidence, the amount of evidence you’d collect is likely to be so small that it hardly justifies the effort of conducting the experiment.
It’s true that you could get evidence from such an experiment which would allow you to update your posterior (although if you’re using significance testing like most experiments, you’re very unlikely to achieve statistical significance, and your experiment almost certainly won’t get published.) But even if you’re doing it purely for your own evidence, the amount of evidence you’d collect is likely to be so small that it hardly justifies the effort of conducting the experiment.