I think the goal should not be to lower the standards for everyone, it should be to help bring people up to the basic standards.

The more often people write informally, the more difficult it is for non-native speakers to learn correct grammar. I almost always use full sentences and correct punctuation in all forms of communication. But I make sure to always write correctly when I'm communicating with non-native speakers. I am doing them a disservice, otherwise. And it's also frustrating to me when I'm learning a language and what I'm reading from native speakers is below even my capability.

Also, I think there's a difference between making mistakes in a foreign language, and being lazy or not caring. For example, capitalizing the first letter of a sentence or the word "I" is something that 99% of people know they should do. So that mistake is not usually due to lack of fluency in a language.