VLSI channel routing: Why only route through channels?
We can, and we do, route higher metal layers over the standard cells. You may be looking at an older reference. Back in the old days we had only two layers of metal for routing. The first metal layer was used extensively inside the standard cells and typically formed fat horizontal power rails as well. So, an empty "routing channel" was left between rows of cells. Within this routing channel we used metal 1 for horizontal tracks and metal 2 for vertical tracks. The vertical metal 2 could pass over the cells and connect to any desired metal 1 track below.

Polysilicon could also be used for short wiring tracks, but it had relatively high sheet resistance and capacitance. The resistance problem was largely solved when we learned how to add a silicide layer to the poly, but that wasn't available back in the day.

Once three or more metal layers became available it was possible to do horizontal and vertical routing without using metal 1, so the dedicated routing channels were no longer necessary.