How do I enable key repeat on iOS?
The other answers here are inaccurate. The correct answer is "sort of"

@MichaelGoerz Comment is correct. There seems to be a bug in iOS where key repeat only works for certain keys instead of all keys as expected. For example backspace will repeat per your settings but "w" won't. I recommend filing a bug report with Apple at https://bugreport.apple.com in an effort to prod them to fix this. This bug is highly irritating especially when using remote desktop tools where holding down a key might be required. 

I occurred to me that this may also be by design, an attempt by Apple to be "helpful" by only allowing the most commonly used repeating keys. Due to the fact that the Settings->General->Accessibility->Keyboard->Key Repeat menu makes no mention of this I am treating it as a bug.