  White dwarfs (WDs) have roughly Earth-sized radii - a fact long recognized to
facilitate the potential discovery of sub-Earth sized planets via transits, as
well atmospheric characterization including biosignatures. Despite this, the
first (and still only) transiting planet discovered in 2020 was a roughly
Jupiter-sized world, found using TESS photometry. Given the relative paucity of
giant planets compared to terrestrials indicated by both exoplanet demographics
and theoretical simulations (a "bottom-heavy" radius distribution), this is
perhaps somewhat surprising. Here, we quantify the surprisingness of this fact
accounting for geometric bias and detection bias assuming 1) a bottom-heavy
Kepler derived radius distribution, and 2) a top-heavy radial velocity inspired
radius distribution. Both are concerning, with the latter implying rocky
planets are highly unusual and the former implying WD 1856 b would have to be
highly surprising event at the <0.5% level. Using an HBM, we infer the implied
power-law radius distribution conditioned upon WD 1856 b and arrive at a
top-heavy distribution, such that 0.1-2 REarth planets are an
order-of-magnitude less common than 2-20 REarth planets in the period range of
0.1-10 days. The implied hypothesis is that transiting WD rocky planets are
rare. We discuss ways to reconcile this with other evidence for minor bodies
around WDs, and ultimately argue that it should be easily testable.
