The US Army wanted a lighter & easier to build regiment/battalion support weapon than the French 37mm gun. Goddard gave them a working prototype that could carry a 1918 version of the HE rifle grenade warhead a fair distance. The Army said thanks and shelved the thing in 1919 & did not pick up on the concept again until 1941. I have no idea how the Army would have deployed Goddards rocket gun had it gone into production in 1919. Perhaps like the 37mm gun in a regimental support company, then in the battalion as more became available? They'd have been useful for harassing MG nests or sniping at bunker & pill box embrasures? Maybe supplementing MG fires with volleys of HE rounds? Not many panzers to attack in 1919.
We never saw or trained with rifle grenades during my USMC years. I doubt they were in the inventory then. The M203 was the light HE tosser. At one point we were equipped with three per squad or nine per platoon. The 60mm mortar had been reissued then as well, so the 'rifle' company had 30 tubes minimum for hurling HE & smoke rounds about the landscape.