"Secretary, write quickly!"
Translation:Sekretario, skribu rapide!
-isto usually forms nouns from verbs.
So a sekretisto would be somebody who professionally does sekreti, which apparently means "make a secret out of something, speak secretly".
But the short answer is: because Esperanto decided to borrow a separate root for this rather than derive a word from an existing root.
(Why is it "koridoro" when there is a root "kuri"?)
It's not generally clear what the obvious meaning is of a verb made from a noun.
Verbs can be made more freely from adjectives, so sekretarii might be considered to mean esti sekretaria (be secretarial - e.g. "a secretarial position" or "a secretarial desk").
In which case a sekretariisto would be someone who is secretarial, professionally. A bit odd.
And not particularly clear or common.
So, possible if you want to play with the language or show people how clever you are; less useful if you want to communicate with people.