should not be more natural in this case "scrivono alcune lettere"? I undestand that eating from something like "mangiano del pane" can be interpreted as eating some amout but in this from it is somehow strange for me if it is regarded to as some letters....
The compound preposition is used as a plural for the indeterminate article: "ho un cane" (I have a dog), "ho dei cani" (I have some dogs). You're right that alcuni/e is a better translation for "some", but "some" is the closer English gets to del/della/dei/delle.