Compounding does not start from bare stems. It starts from a real phrase, two padas that could stand in an ordinary sentence, each already declined. 2.1.1 requires the two words to be समर्थ — mutually construable, capable of modifying one another — and 2.1.4 says the joining happens between words that end in सुप्, the ordinary nominal case endings.
Only once that phrase exists does 2.4.71 act: it elides the सुप् of both. Not one — both. And 1.2.46 gives the result its own status: कृत् words, तद्धित words and समासs are all counted as प्रातिपदिक — a nominal stem in its own right, exactly like गृह or पति on their own, ready to take one fresh ending when the sentence actually needs one.
Compounded, both endings go, and becomes one word: — declinable again, but only once, as a whole.