With wooden soles for stiffness and so the nails would anchor– this was before my time. I started cycling at the tail end of the toe clips era, but had Nike cycling shoes with nylon soles and slots to screw a slotted plastic cleat into to would fit over and around the edge of a pedal cage before tightening the straps. I modified the cleats for rotation by enlarging the cleat slot and filing angles in the ends.

Do we have to go back to those days? Nail on was the worst.

https://www.classicsteelbikes.com/product/ta-anquetil-piste-cleats-plates/

Gotta meet the expectations of the vegan crowd

They do go through the body of the pedal, not the outer cage

For those who don’t know, you used to have to nail on cleats(for toe clips/ straps) way before clipless pedals came about. These cleats were two piece which would provide a slot for the pedal frame to fit into. The clips and straps would just hold your foot to to the pedal. I’m not sure if you can even find these “nail on cleats” anymore.