I couldn't imagine writing without at least attempting to use proper grammar. Especially in German where ignoring capitalization makes a difference of night and day.
My reasoning has been similar to the one of the author, but more on a "positivity" than a plain productivity level. If it's easy for others to read my messages and not having to puzzle over them, I hope that it will leave them with overall a more positive association of writing/communicating with me. And that not only goes for professional texting, but writing with friends (or dating) as well. I know it won't always come out perfect, but overall I think it shows some level of respect towards the other person.
Periods + capitalization (when writing in English) over IM comes across as "cold" to me, whether or not someone's using emoji; unless they're above a certain age, of course.
The main one that trips me up is when people use acronyms I'm not familiar with. Then I try to Google for them, but sometimes it's hard to find, or ambiguous.
Which makes me wonder if the author of the article used the noun "ask" deliberately, and whether it simply means "question".
Using that word out of carelessness in an article about the clarity of communication, with a mention of non-native speakers would be ironic.