The ocean has:
- specific heat of ~4J / g / K
- a mass of ~1.4 x 10 ^ 24 g
- a much lower viscosity than rock and soil, so it can convect on meaningful timescales
As such, it completely and utterly dominates short-term thermal storage on Earth's surface, and damps short-term fluctuations.
100%, no argument, you're right there. "Continental" desert climates far from the ocean are evidence of this.
But the atmosphere doesn't need thermal mass to warm the surface, it needs only finite optical depth at IR wavelengths, non-zero emissivity, and a nonzero kinematic viscosity.
Its thermal mass is insignificant compared to the ocean, just as your blanket's thermal mass is incomparably less than yours.
So your blanket, like the atmosphere, quickly heats up and starts conducting and radiating your own IR back at you.
A greater thermal mass would delay this, and make it LESS efficient at retaining heat over 24hrs.