[jakobnev]

Counterflow heat exchangers are most effective when both fluids have large temperature changes as they pass through the heat exchanger. Automotive cooling systems have relatively small temperature change on the water side, therefore counterflow has small benefit.

Good point, depending on how small, it might not be worth the effort.

If you have the space to make air flow as shown, then you have the room to make the radiator thicker.

It's not that practical to thicken a radiator DIY-style, you have to replace it. (or add one in front) Ducts are much easier to build. (and more often free)

There is an excellent book that covers this subject: Compact Head Exchangers, by Kays and London.