Because they're sensible heat machines, instead of latent heat machines. In a perfect frictionless vacuum, both of these can achieve the same theoretical efficiency. In practice, not so much. In particular, the isothermal heat exchange of the ideal Stirling cycle requires heat exchangers with no thermal resistance (and therefore no temperature difference). A latent heat pump has a much easier time to very closely approximate isothermal heat exchange because condensation/evaporation temperatures at a given pressure are essentially constant.
What is the back of the envelope efficiency penalty we're talking about here?