Aaron Werlen, Caroline Dorn, Remo Burn, Hilke E. Schlichting, Simon L. Grimm, Edward D. Young

Recent claims of biosignature gases in sub-Neptune atmospheres have renewed interest in water-rich sub-Neptunes with surface oceans, often referred to as Hycean planets. These planets are hypothesized to form beyond the snow line, accreting large amounts of H$_2$O >10 wt%) before migrating inward. However, current interior models often neglect chemical equilibration between primordial atmospheres and molten interiors. Here, we compute global chemical equilibrium states for a synthetic population of sub-Neptunes with magma oceans. Although many initially accrete 5-30 wt% water, interior-atmosphere interactions destroy most of it, reducing final H$_2$O mass fractions to below 1.5 wt%. As a result, none meet the threshold for Hycean planets. Despite that, we find H$_2$O-dominated atmospheres exclusively on planets that accreted the least ice. These planets form inside the snow line, are depleted in carbon and hydrogen, and develop small envelopes with envelope mass fractions below 1%, dominated by endogenic water. In contrast, planets formed beyond the snow line accrete more volatiles, but their water is largely converted to H$_2$ gas or sequestered into the interior, resulting in low atmospheric H$_2$O mass fractions. Most H$_2$O-rich envelopes are also fully miscible with H$_2$, making a separate water layer unlikely. Our results topple the conventional link between ice accretion and water-rich atmospheres, showing instead that H$_2$O-dominated envelopes emerge through chemical equilibration in hydrogen-poor planets formed inside the snow line.