[en] The grain boundaries (GBs) of high-temperature superconductors (HTSs) intrinsically limit the maximum achievable inter-grain current density ($J_{\mathrm{c}}$), when the misalignment between the crystallographic axes of adjacent grains exceeds a certain value. A prominent effect resulting from large-angle GBs is a hysteresis of $J_{\mathrm{c}}$ between the increasing and decreasing field branches. Here, we investigate this feature for K- and Co-doped Ba-122 polycrystalline bulks with systematically varied grain size and find that the widely accepted explanation for this effect—the return field of the grains—fails. We use large-area scanning Hall-probe microscopy to distinguish $J_{\mathrm{c}}$ from the intra-granular current density ($J^{\mathrm{G}}$) in order to clarify their interactions. Measurements on Ba-122 bulks reveal that a large $J_{\mathrm{c}}$ results from a small $J^{\mathrm{G}}$ as well as small grains. An extended version of the model proposed by Svistunov and D’yachenko is successfully applied to quantitatively evaluate this behavior. The excellent agreement between the model and experiments suggests that the GBs limit the macroscopic current in all of the samples and that the inter-grain coupling is governed by Josephson tunneling. The predictions of the model are promising in view of realizing high-field HTS magnets. Our main result is that the field dependence of the $J_{\mathrm{c}}$ of an untextured wire can be significantly reduced by reducing the grain size, which results in much higher currents at high magnetic fields. This result is not limited to the investigated iron-based materials and is therefore of interest in the context of other HTS materials. (paper)