According to Microsoft's documentation,
[StorageClass is a] modifier that redefines a function declaration. inline is currently the only modifier value. The modifier value must be inline because it is also the default value. Therefore, a function is inline regardless of whether you specify inline, and all functions in HLSL are inline.
If all functions in HLSL are inline, why even have the modifier? If the only modifier value is inline, why even have the StorageClass part of the function declaration?