If Germany invaded trough Switserland in WWI

One of the reasons Belgium is better than Switzerland as an invasion corridor is the rail system. The rail net from Germany through Belgium to France is a lot denser than Germany through Switzerland to France, and the topography makes doing damage easier in Switzerland easier and repairing damage easier in Belgium (you can replace bridges a lot faster than tunnels or long stretches of trestle). The only way you can supply a rapid advance in 1914 is using rails, trucks are limited and roads crap and horses move too slowly. Going through Switzerland is just a bad idea. As far as threatening Italy goes, remember Italy was part of the Triple Alliance, although they bailed.
 
WI an Austrian official discusses - with a Swiss official - an invasion of France via Switzerland. They agree that such an invasion would be slow, bloody and ruinous to the Swiss economy.
Kaiser Wilhelm II cheerfully proposes a less harmful alternative. If Switzerland allows sealed trains to run from Basel to Geneva - for a week - no Swiss citizens will suffer. The French-speaking Vallee is the only viable invasion route through Switzerland. The wide, gently sloped Vallee only has a few lakes and small rivers. It parallels the French border in Western Switzerland. To the west, it is shielded by the Jura Mountains.

A week later, German trains quietly roll the length of the Swiss Valley and burst into France beyond Geneva. Next thing you know, German cavalry are galloping around Lyons.
As the southern invasion distracts the French Army, German troops breach the border at several places. After one week, German railroads establish direct links from Baden-Wurtembourg to Lyons.
The Vallee Route is abandoned.
 
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