Why would you want that? Handwriting is slow, certainly slower than the keyboard iOS provides. I’m honestly puzzled why handwriting was ever a favored input method.

You are right about speed. However, I would like to have handwriting simply for symbols and drawing (i.e. mindmapping). How are you going to enter math formulas faster with a keyboard than a pen? Same goes for marking and annotating things. IMO, precision and speed for marking/annotating is pretty bad with iOS.

But I don't see how apps like Omnifocus can make use of it.

You'd need a thin stylus for that, and Apple doesn't ship one which means they're not going to built it into the OS.

But surely it wouldn't be too hard (where too hard means technically infeasible) to create an application based on hand-written input (Graffiti or Rosetta/Inkwell-type technologies).

And there are indeed apps that do that. (I don't know the name(s), but I've seen at least one running on a friend's iPad.)

Maybe because just about everyone knows how to do it, and because it's quieter than tapping on a screen or keyboard?

That's not to say it's the optimal method of input, but either is voice. There are use cases where writing or voice may be better than typing.

While writing might be a nice additional feature, I can certainly understand why Apple didn’t build iOS around it. (In the current climate this probably also means that handwriting won’t come to iOS anytime soon.)

I think we can thank RIM for that. While they were not the first, they arguably made the QWERTY keyboard ubiquitous and (for the first time) more than tolerable on a phone sized device.

iOS has had a handwriting-based keyboard for Chinese since iPhoneOS 2.0.

But I'm guessing drawing letterforms with your finger isn't a very enjoyable input method, and most of the iPad styluses available aim at replicating a finger (since that's what most applications expect).

Actually for drawing Chinese characters it's not that bad. I plan to get an iPad for my parents so they can draw Chinese characters instead of learning how to type (there are many older generations in China who cannot type Chinese on a computer because they don't know how to do that).

I just wish the character recognition could be better.

Oh yes, sorry for the lack of precision, I meant "for western-european languages" (or more precisely for languages with a fairly low number of graphemes), for Chinese or for Japanese Kanji it makes a lot of sense to ask for tracing as providing keyboard systems with good/easy access to thousands of graphemes is not easy.

Though I believe Japanese have a system for such a thing, which they use on regular QWERTY keyboard, my sister demonstrated it to me (you basically type phonetics and it builds graphemes/characters on the fly, something like that). For that reason (and because japanese people are used to that kind of input) iOS has a qwerty (romaji) and a 10key japanese keyboards but I don't think it has a handwritten one (it has 8 different Chinese keyboards, 3 simplified [with "handwriting" and "stroke" versions] and 3 Traditional [Handwriting, pinyin, zhuyin, cangjie and stroke]).

Not yet, but Mac OS X does.

Did the Newton?

:-)

Not part of the OS per se. Part of the platform, yes, but there were plenty of apps that never used handwriting recognition.

[Near as I can tell, the only association with Newton is the use of an ARM. I sure wouldn't use NewtOS on anything modern, even as cool as NewtOS was in its day.]