They normally construct quads out of thin copper wire. Then they expect the quad to outperform the Yagi. Rod elements, in Yagis, do not. As David Jefferies has explained, the coupling is via the corner currents and the non-radiating wires which connect the radiators. The lesson we learned from this is that the ideal element spacing in quads has to be far wider than published in the old, stale, literature.
Many benefits accrue from proper coupling.
The current division is important since the losses of such an antenna, especially on the low HF bands, are a function of the square of the element currents. In the case of parasitic rectangles, we can increase the gain significantly on 80 meters simply by using the proper element spacing and reducing the loop losses. We can also almost double the SWR bandwidth as compared to that of a single loop. As LB Cebik has pointed out, one of the selling points of quads is that they are lower in Q than Yagis. Their SWR BW is far wider.