  Electroweak baryogenesis (EWBG) is sourced by nonstandard $CP$-violating
interactions of the Higgs boson with fermions, usually taken to be the top
quark, enhanced by its large Yukawa coupling. Numerous papers have studied EWBG
sourced by lighter fermions, including the tau lepton and off-diagonal quark
mass terms. We critically reassess the viability of EWBG in these scenarios,
comparing the predictions based on the semiclassical (WKB) formalism for the
source term to those from the VEV insertion approximation (VIA), using updated
values for the collision terms, and clarifying discrepancies in the definition
of the weak sphaleron rate. The VIA systematically predicts a baryon asymmetry
that is orders of magnitude larger than the WKB formalism. We trace this to the
differing shapes of the $CP$-violating source terms in the two formalisms,
showing that the additional spatial derivative in the WKB source term causes
large cancellations when it is integrated over the bubble wall profile. An
important exception is a source term from $c$-$t$ quark mixing, where the WKB
prediction also allows for a realistically large baryon asymmetry. In contrast,
the analogous $b$-$s$ mixing source is found to be orders of magnitude too
small.
