I can not see any advantage in changing the methodologies that have been developed and used over centuries.

Nobody I know shaves with the toe leading. You shave with the heel leading and with a downward (or upward or sideways) sawing stroke. Well actually you can shave however you like, I'm just talking about the "normal/natural" way folks shave.

Have you ever tried to saw a piece of wood with the toe leading. (Western type saws).

The X pattern with the heel leading puts a scratch pattern that allows a sawing type action as you draw the blade down the face. Toe leading doesn't do this. It does the reverse and that will give a less comfortable shave.

The stropping process (cleaning with leather) should also be with the heel leading. This allows the fine nap on the leather to open the teeth on the blades edge and remove any oxidation by brushing it off the edge and helping the edge to be smoother thereby and realigned. Heel leading forces the nap through the teeth giving a better scrubbing/cleaning action than say toe leading that just goes with the flow and doesn't release the rust so effectively.

The process of honing and stropping is designed to put a serrated cutting edge at a 45 degree angle to the cutting surface and present the face with a smooth edge that glides effortlessly over the skin which has been made tender by the exfoliating action of the cutting edge cutting away the stubble and any loose dead skin.

This is not my perceived wisdom, but just a summary of the many descriptions I have read in barbers manuals, that all explain the process in a similar manner.

It makes total sense to me at least.