I believe this was adapted from the regulation army uniform of Europe - where the leather neck guard was used to keep their heads high etc. Certainly, the Royal Marines and British Army regiments had them.

In the late 18th and early-mid 19th centuries, leather neck stocks were a fairly common item of uniform, at least in British infantry units. So the Marine's adoption of leather stocks was as much a nod to contemporary military fashions as it was to anything else. Officers also thought the neckpieces made Marines have a more military bearing and that they offered some protection from neck injuries. As military fashions changed in the mid-late 19th century, the stocks were quietly dropped. Neck stocks were discontinued as part of the Marine uniform in the 1870s.

There's a rumor circulating that leather neckwear was temporarily reissued during the Philippine Insurrection to provide protection from the Bolo knives and machetes, although I've yet to see concrete evidence to back this claim.