Seriously, there is no reason that they shouldn't have them.
The US didn't use snipers like other Britain, Germany, and Russia did. Making Snipers in those countries meant extensive training in marksmanship, stealth, camouflage, and such. Making an American Sniper was simply taking the most accurate soldier and giving him extra marksmanship training. Afterward, they usually operated as part of an Infantry Platoon and wore the same uniforms and used to the same tactics.
In the end, Jaeger Light Infantry squads are more like US Snipers than Pathfinders are. There is an unused weapon rack for M1 Garand Snipers, so it's a shame that was scrapped. Also it's interesting they chose the Garand, since the Springfield was the assigned weapon for most American Snipers.