Serenity Caldwell, writing for iMore, would like to see iOS gaining handwriting recognition at a system level, especially now that iPad users have the Pencil:

There are plenty of reasons why Apple hasn’t yet implemented system-level handwriting recognition in iOS: For one, you need an exceptionally good pen input, and — until the introduction of the Pencil — no third-party stylus had the precision or the lag reduction to be a truly useful tool.

There’s also both the processing power and stigma to consider. Like Siri, handwriting recognition works as a transcription service; in order for it to translate your physical marks into typed characters, however, it needs a substantial dictionary and the power to transcribe your words using your phone’s processor or online servers. That means more cloud infrastructure or more powerful iOS devices — or both — as well as the engineers to craft a smart dictionary.

If Apple does add this to the Notes app – and I believe it would make sense – OCR for images and documents would also be another welcome text-related improvement.