Re: English, bad English and AInglish
We've had adequate machine-generated English prose for years - in fact, for nearly two decades. Philip Parker's system has generated thousands of published works under the ICON Group imprint since his patent was granted in 2007; he'd been working on it since around the turn of the century. That's thousands of computer-generated books that people have paid money for. And who knows how many his private report-generating concern EdgeMaven Media has produced on top of that.
It's hard to know exactly how many distinct works have been churned out by Parker's system, since most are print-on-demand and many of the listings may refer to books that have never been generated. According to media reports, ICON Group will list a title when they believe they have the data necessary to create the associated book.
These books are, admittedly, rather dry. But it seems they're perfectly readable.
Then we have Narrative Science, which for several years has produced computer-generated articles for major magazines. The AP wire service has used NLG (Natural Language Generation) software from Automated Insights to generate wire articles since 2014, and apparently Yahoo uses Automated's tech to produce recaps for fantasy football.1 And so on.
NLG is actually quite easy within many constrained domains. But these NLG systems work quite differently from complex NN architectures which are attempting to generate realistic English prose based on unsupervised learning. Comparing them is a bit like comparing a table saw to a humanoid robot trying to teach itself to cut lumber using a handsaw.
But that said, we have quite effective technology for automatically generating realistic, useful natural-language prose, and have had for some time.
As for the point of your post: You'd really want a methodologically-sound study conducted by linguists with expertise in the appropriate areas for this, but I think your assumptions aren't well-founded. I've known a number of ESL (English as a Second Language) writers, and a number of TESOL professionals; and I've read a bit of TESOL theory and research. Second-language writers don't tend to be algorithmic. They're as prone to unexpected word choice as they are to using the expected word, because their vocabulary is more limited (and thus less precise) and they have less familiarity with idiom. While they may get inflections and particularly irregular word forms wrong, their grammatical structures are often more limited but also more formal than those of native speakers - they have less experience to tell them when native speakers are likely to bend the rules.2
Even a relatively simple classifier like an SVM consuming chunked input (so you get some phrase-level structure, not just unigram) could probably do a decent job of distinguishing ESL and OpenAI candidates.
1I look forward to the day when every aspect of sports, from participation to consumption, is fully automated, and humans are not involved at all.
2Of course there are no rules as such, but for the sake of the point we'll pretend there are.