The fact that H is interesting enough for you to be considering the question at all (it’s not some arbitrary trivium like the 1923th binary digit of π, or the low temperature in São Paulo on September 17, 1978) means that it must have some relevance to the things you care about.
If there’s not much information about H directly, then H is highly reflective of one’s general priors. In domains where people care about estimating each other’s priors (e.g. controversial political domains), they might jump onto H as a strong signal of those priors, but the very fact that there’s not much evidence about H also puts bounds on how much effect H could have (because huge effects propagate somewhat further and thus provide more evidence, yet we know by assumption there isn’t much evidence about H). When H finally gets settled, it likely becomes some annoying milquetoast thing that shouldn’t really validate either prior (but often can be cast as validating one side or the other).
If there’s not much information about H directly, then H is highly reflective of one’s general priors. In domains where people care about estimating each other’s priors (e.g. controversial political domains), they might jump onto H as a strong signal of those priors, but the very fact that there’s not much evidence about H also puts bounds on how much effect H could have (because huge effects propagate somewhat further and thus provide more evidence, yet we know by assumption there isn’t much evidence about H). When H finally gets settled, it likely becomes some annoying milquetoast thing that shouldn’t really validate either prior (but often can be cast as validating one side or the other).