Many people focus on using "proper grammar" because when they have a difficult time understanding something, grammar is an easy thing to blame. However, when a writer with poor skills in sentence structure, spelling, and comma usage takes the time to construct an effective outline, many readers fail to notice the lack of skills in grammar.
Likewise, many writers who feel they have poor skills focus only on their own ability with grammar. Instead, writers should make sure they have solid ideas and an effective outline before working on anything as minor as mechanics. Then, after they've gotten everything down on paper, they can work on making what they wrote easier to understand. That's all grammar is for, really -- to help you make other people understand what you want them to. Using the proper 'register' or 'variety' are just buzzwords. When you know what you are saying and understand who you are saying it to, you'll do just fine.