As far as I know, the only way we currently know how to prove Borel determinacy in $\mathsf{ZFC}$ is to go through unravelability (a rather technical property whose definition can be found in Martin's A purely inductive proof of Borel determinacy). Unlike determinacy, however, unravelability is in general still somewhat mysterious. Additionally, most determinacy proofs in other contexts (e.g. analytic determinacy from sharps) do not involve unravelability at all.
I'm curious whether the use of unravelability in the Borel setting is in principle avoidable. Specifically, my question is whether the following theory is consistent: $$\mathsf{ZC+\Sigma_1Rep+\mbox{Every Borel set of reals is determined}+\mbox{There is a non-unravelable Borel set of reals}}.$$
Here $\mathsf{ZC}$ is $\mathsf{ZFC}$ without replacement/collection; in my experience this theory is a bit pathological, so I've added back in $\Sigma_1$ replacement. Note that since $\mathsf{\Sigma_1Rep}$ doesn't let us iterate powerset through the ordinals, Friedman's theorem applies and $\mathsf{ZC+\Sigma_1Rep}$ does not prove Borel determinacy.
