Why don't we say "subhanahu wa ta'ala" after saying "assalamu alaikum wa rahmatullah"?

After saying Allah, it seems we're encouraged to say "subhanahu wa ta'ala" (meaning "the most glorified, the most high"). However, there seems to be exceptions to this, e.g., when we say "assalamu alaikum wa rahmatullah" (meaning "peace and mercy of Allah be upon you"). We say this e.g. at the end of salah prayer. **Question**: Why don't we say "subhanahu wa ta'ala" after saying "assalamu alaikum wa rahmatullah"?