What are the advantage of adding interactive variable over subsampling in drawing conclusions?

There are two main advantages of adding interaction variables over subsampling are: (1) having higher sample size, leading to higher precision and (2) higher degree of freedom.

Nornal regression equation:

Dependent_variables= pt + Independent_variables + fixed effects + error term (1)

Adding interaction variable equation:

Dependent_variables= pt + developed_dummy*pt + Independent_variables + fixed effects + error term (2)

I am wondering what is the advantage of the explanation of adding interaction variables over subsampling (if having)? Array

I know how to explain the second regression result:
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