Abstract Observed rotation curves in star-forming galaxies indicate a puzzling dearth of dark matter in extended flat cores within haloes of mass ≥1012M⊙ at z ∼ 2. This is not reproduced by current cosmological simulations, and supernova-driven outflows are not effective in such massive haloes. We address a hybrid scenario where post-compaction merging satellites heat up the dark-matter cusps by dynamical friction, allowing AGN-driven outflows to generate cores. Using analytic and semi-analytic models (SatGen), we estimate the dynamical-friction heating as a function of satellite compactness for a cosmological sequence of mergers. Cosmological simulations (VELA) demonstrate that satellites of initial virial masses >1011.3M⊙, that undergo wet compactions, become sufficiently compact for significant heating. Constituting a major fraction of the accretion onto haloes ≥1012M⊙, these satellites heat-up the cusps in half a virial time at z ∼ 2. Using a model for outflow-driven core formation (CuspCore), we demonstrate that the heated dark-matter cusps develop extended cores in response to removal of half the gas mass, while the more compact stellar systems remain intact. The mergers keep the dark matter hot, while the gas supply, fresh and recycled, is sufficient for the AGN outflows. AGN indeed become effective in haloes ≥1012M⊙, where the black-hole growth is no longer suppressed by supernovae and its compaction-driven rapid growth is maintained by a hot CGM. For simulations to reproduce the dynamical-friction effects, they should resolve the compaction of the massive satellites and avoid artificial tidal disruption. AGN feedback could be boosted by clumpy black-hole accretion and clumpy response to AGN.