I know that verbatim has a Latin origin, but why is it not spelled verbatum?
English does not seem to have many Latin words that end in ‑im.
The reason that it’s spelled verbatim is because the word was copied from Latin verbatim. It was not respelled. It would be a travesty to use some other spelling for that word, for such a respelling would put the lie to the very word itself.
Other words of that form attested by the OED include alternatim, gradatim, guttatim, literatim, nominatim, punctatim, punctuatim, seriatim, stillatim, and syllabatim.
The ‑atim suffix in Latin is an adverbial suffix meaning ‑by‑ that noun. Each of those means by that noun, or noun by noun, making verbatim word by (or for) word, literatim letter by letter, et cetera.