Why are Dalton and Grams / Moles not equivalent units?

I never heard the unit "dalton" before, but according to Wikipedia, 1 dalton equals $1.66053904\times 10^{−27}\, \mathrm{kg}$. That's what Mathematica says, too:

UnitConvert[Quantity["Daltons"], "Kilograms"]

1.6605390*10^-27 kg

But it's weird that neither UnitConvert nor UnitSimplify seem to know that mol is a dimensionless unit, so it could be replaced with a dimensionless constant.

If I explicitly ask for a unitless value using UnitSimplify with the option UnityDimensions, I get 1 as a result, which seems strange to me:

UnitSimplify[Quantity[1, "Moles"], UnityDimensions -> {"AmountUnit"}]

1

As nikie has pointed out, Mathematica considers the Dalton to be a unit of mass. It is also synonymous with the unified atomic mass unit (u).

UnitConvert[Quantity["Daltons"], "u"]

1.0000000u

Mathematica also distinguishes between Molecular Mass and Molar Mass and the default unit for MolecularMass appears to be unified atomic mass unit (u) rather than the Dalton

{#, UnitConvert[#, "Daltons"]}& @ ChemicalData["Water", "MolecularMass"] 

{18.0153u,18.0153daltons}

Compare with:

{#, UnitConvert[#, "Daltons"], UnitConvert[#, "u"]}& ChemicalData["Water", "MolarMass"]

{18.0153g/mol,1.08491*10^25daltons/mol,1.08491*10^25u/mol}

In addition:

{#, UnitConvert[#, "Daltons"]} &@ ChemicalData["Water", "MolecularMass"]    // QuantityUnit

$\{\text{AtomicMassUnit},\text{Daltons}\}$

and

{#, UnitConvert[#, "Daltons"], UnitConvert[#, "u"]} & @
ChemicalData["Water", "MolarMass"] // QuantityUnit

$\left\{\frac{\text{Grams}}{\text{Moles}},\frac{\text{Daltons}}{\text{Moles}},\frac{\text{AtomicMassUnit}}{\text{Moles}}\right\}$

There is also Kilodaltons, of course:

ProteinData[6400, "MolecularWeight"] // UnitConvert[#, "Kilodaltons"] &

33.02400kDa

Despite the wikipedia quote, I don't think biochemists use the definition 1 Da = 1 g/mol. For a good discussion of the Dalton and the confusion it can cause, see To land on a dalton by Susan Dewhurst, available here

Yes, they are:

   << Units`
    Convert[1 Dalton, Gram/Mole]