having to march into the breach (going beyond the reach of their mainly wired comms and the extent of their rail network), supplied almost exclusively by horse, and the defenders rushing to block the gap in their line, usually via train, and on territory where they still had full access to their comms.

Naturally, in this race, the people riding trains tended to beat those marching on foot - and hence a huge advantage of maneuver for the defender, who also enjoyed greater cohesion and clarity of purpose due to the possession of a functioning wire network.

Actually most of the transit to the battlefield was on foot, regardless of attack or defense. The issue was largely with supply lines for the attacker. It should also be noted that motorized transport made huge strides during WWI, and by the end horse transport was not the sole means of moving supplies and troops.

The decisive weapon of WWII was the automobile - not tanks, but the humble truck (for without trucks to hump their gas and ammo, tanks were relatively hobbled). With the advent of fully motorized units, the little successes which in WWI frequently petered-out after a few kilometers could be turned into scything penetrations stretching over hundreds of kilometers, with a minimal diminution of fighting power as the mighty truck tirelessly hauled supplies and reinforcements at speeds comparable to a train, to places the tracks could not reach. Units on the march could be guided and coordinated with relative ease by radio, instead of suffering the inertia caused by having to wait for runners or wire to be laid behind the advancing soldiers.

Not really; aside from the whole issue of 'decisive weapons', when weapons systems ie the armies themselves are what win wars, the automobile wasn't the decisive weapon. The need for spare parts, repairs and refueling added new limitations to the means of transport, and horses and mules were better off road than most trucks and cars. Strategic and Operational mobility was still largely dependent on rail and maritime transport, with getting the French railways back up and running being one of the primary goals of the Allied Expeditionary Force after the breakout from Normandy. As for transport from the Operational level down, the Italian, French, German and Soviet Armies all relied on horse transportfor various tasks.

It really isn't until the post-WWII era, with transistor radios and more motorized/mechanized armies, that rail and animal based transport could be said to have been completely subsumed.