A few things. Egyptian went through a number of phases as a language. Old Egyptian and Middle Egyptian are the most similar, although Old Egyptian's writing system is a bit clunky. New Egyptian is syntactically radically different, but its lexicon is more or less the same, and the major changes in the writing are the simplification of some spellings to reflect changes in the pronunciation of the language. Understand, however--and this is crucial--that the hieroglyphic script was not the "everyday" script. Relatively few scribes could even write more than a few words in the hieroglyphic script, and it was reserved for inscriptions and sacred texts. It was, therefore, extremely conservative. The "classical" Middle Egyptian was preserved as a standard literary language well into the New Kingdom, and New Egyptian never fully replaced Middle Egyptian--even in texts that are clearly in New Egyptian it's very easy to find the strong influence of Middle Egyptian.

Moreover, we don't just copy-and-paste the Rosetta stone's vocabulary and syntax, that's not what was gained from deciphering the text. The important breakthrough was the ability to identify the uniliteral and later multiliteral signs--this is Champollion's gloss of the uniliteral signs (some of his values I believe are wrong, as a number of those signs are multiliterals in Middle Egyptian--I'm not positive about New Egyptian). The values of the phonetic signs generally did not change from Middle Egyptian to New Egyptian. We find changes in spelling, and patterns like the dropping of the feminine ending .t, but these are predicable patterns that we recognize. The identification of the uniliterals and multiliterals allowed us to reconstruct phonetically (roughly) the values throughout all periods of the Egyptian language. It's like learning the Roman alphabet--you have to learn the letters before you learn Latin, but you can learn the letters in Italian and then apply them to Latin