Why does the noun "assumption" lose the "p" when it goes to verb form: "assume?"

Nouns such as "consumption," "assumption," and "presumption" all have the letter "p" but their verb forms, "consume," "assume," and "presume" do not.

Why is that? Is there a simple linguistics reason?

The reason is simply that the stems of these verbs (which come from Latin) did not have a /p/ sound. The [p] was inserted before /t/ in Latin for much the same reasons that English speakers tend to insert a [p] between /m/ and /t/ in words like "dreamt" (from the stem "dream", not *"dreamp").

Latin spelling is for the most part phonetic, so in Latin the insertion of the sound [p] could be indicated in writing by the addition of the letter "p". (It wasn't always: "mt" and "mpt" cooexisted as variant spellings in Latin. But the "mpt" spellings came to be established in English.)

Since there is no "t" in consume, assume and presume (or their Latin sources), there is no "p" either.