Badness and non-stationarity for dfg groups

Let $H$ be a group definable in an $o$-minimal structure or a $p$-adically closed field, and assume that $H$ is a $\mathrm{dfg}$ group. Say that $H$ is bad when it has the badness property defined in the paper, namely the relevant strongly $f$-generic behavior fails as specified there. Badness conjecture. The group $H$ is bad if and only if $H$ is non-stationary. The paper has established badness for the displayed examples of the additive square and the Borel subgroup, while the equivalence for arbitrary $\mathrm{dfg}$ groups in the stated classes remains open.