On one hand, I can appreciate that it's unpleasant to be put on the spot. Or being forced to use crappy tools. Nobody likes that.
That said, if a person is being considered for a coding job, wouldn't that person want to demonstrate their coding abilities? I mean, assuming they're actually good at coding?
In interviews, I much prefer a concrete problem to an abstract one, and coding problems are typically far more concrete than most other subjects covered in SW dev interviews.
Google Doc is specifically designed for writing and reading and used probably by more people than any other piece of software ever for that task. And you think it's fair to compare it to crayon and napkins? What a world we live in. Programming is often about thinking through the problem, but if you can't separate yourself form your IDE when writing code and it's about syntax then that says more about your style.
While I don't necessarily disagree with the sentiment, I can provide a real life take. Not specific to GDocs, this applies to all browser based editors.
You may usually write code in a terminal based programmer's editor (vim, emacs, ...) and realise the code you've just written is not quite right. You want to delete the last two words. There's even a default and handy keybinding for doing that.
I consider google doc coding an extension of the white board coding, which often happens in pair programming. I do not think it should aim perfectly working code, but at least I would personally expect reasonably good whiteboard coding hygiene from a colleague, at least for a report to the committee.
Like thats how I would feel writing code into freakin google docs during a job interview...with Google.
Tie 1 arm behind by back as the synax goes wonky, I'm fighting the spacing, etc. etc.
Or put mario Andretti into a ford focus, then test his lap times, with 0 warning.
Yuck.