The rule makes perfect sense (and is how I’ve always used it), but this article actually misses a major point which I just learned last week when talking to some native Spanish speakers. In most English speaking countries, the week starts on Sunday. This isn’t the case for many, many other countries though. So saying “this Friday” on a Sunday really really confuses people. That’s exactly what happened to me last week because it was a Sunday and we were talking about a Friday and she got very very confused.

I find Thursday (for this week) and Thursday next (for next week) adequate and am seldom called on for clarification, seems to follow the pattern of the rule (thanks for that) but is more economical.

Another problem is that system requires agreeing on what a week is, and there's disagreement over whether Sunday starts or ends the week.

Yep, same. Or "not this Thursday but the next".