A one-flavour naturalness argument suggests that the Type I seesaw model cannot naturally explain neutrino masses and the baryon asymmetry of the Universe via hierarchical thermal leptogenesis. We prove that there is no way to avoid this conclusion in a minimal three-flavour setup. We then comment on the simplest ways out. In particular, we focus on a resolution utilising a second Higgs doublet. Such models predict an automatically SM-like Higgs boson, (maximally) TeV-scale scalar states, and low- to intermediate-scale hierarchical leptogenesis with $10^3\text{ GeV}\lesssim M_{ N_1}\lesssim 10^7\text{ GeV}$.
Categories: hep-ph