I don't think there should be a writing skill. Not because it's a bad idea, but just because its implementation would be too hard (since it seems to include so much stuff) for the benefits it would bring. Making this ability a 'skill' like the ones we have (sword, armor repairing, etc.) will generate all sorts of questions and complications: what does the skill actually do? (will it just allow you to write and read any book, or something more specific?), what do you earn from upgrading it? (it seems hard to make the skill influence the player's actual writing), how do you get experience in it? (just from editing a book? number of letters? number of game-identified words?). Just to mention a few problems.
An approach that seems to me fairly easier and just as good would be allowing only characters with intelligence above a certain rank (oh, let's say 75) to use books (be it to read or write.)
This would insert the read/write ability, without making it complex at all.
I can already hear the geekiest amongst us claiming reading is not just about intelligence. But then again, how can you require a certain Stat to pick up a weapon when that weapon weighs and is the same size and format (or so it name says) as every other of its family?
The method is just the same with Intelligence requirement to read books. No actual mechanics' format is 100% realistic, not even having a reading skill (like some people mentioned already). The trick here is choosing the mechanism that gives the best change for the least amount of effort.