On 16T freewheels, the size of the driver and the bearings inside the gear limit how small we can make the diameter of the base of the gear. You’ll notice a groove machined on the base next to the teeth which is needed to clear even a 3/32” chain. For an ⅛” chain that groove would need to be a bit deeper to allow the chain to fully seat down on the teeth but we can’t make the groove deeper without sacrificing the strength of the gear. Running an ⅛” chain will prematurely wear out the chain and gear.
On Double freewheels, a wider 1/8″ chain will rub against the adjacent teeth because of the limited space between the two sets of teeth.