I think so, I personally prefer the "look at this already written code, what does it do and can we find any bugs or issues?", less stressful and more collaborative, but good luck getting any non-startup size company to let you do it.

I do something reasonably similar all the time at Google for iOS interviews, few hundred lines of obj-c with some issues in them (actual issues, not typos)

I think this is an excellent idea. Most of your job will be working on already existing code (even if it's written by your former self).