Unitless quantities

Perhaps you can use "Unities" or "PureUnities". The unit "PureUnities" automatically gets turned into a number, while "Unities" needs a UnitConvert:

Quantity[1, "Unities"] //UnitConvert
Quantity[1, "PureUnities"]

1

1

I have confirmation from Wolfram Technical Support that this is a bug. Apparently Quantity[1,""] is being interpreted as the cryptocurrency "LiteCoin." They also claim that the intended method of representing dimensionless units is:

Quantity[a,1]