[couldwejust]

"to" just doesn't make much sense. In a geometric sense, the writing isn't directed, the sending is. The writing is adressed, sure but towards doesn't fit, while it's correct to just adress someone. Just sending someone would be different. With writing, it's underspecified, because there is no "writing someone [down]" :)

In german, write me and write to me also work both, but these are the different grammatical cases dativ and akusativ. There are only four and I'm guessing here. They require the different forms "mir" or "[an] mich". These cases are called the same in english, correct me if I'm wrong.