Along with teaching the points, we should also teach that the points are human tradition, not canon. So students should be taught how to analyze verses to second guess the Masoretes.
I tend to agree with that. I don't buy the view that some have held, that the points were passed down from Moses, or that the Masoretes were divinely inspired. I do believe however, to the extent that they correctly preserved and passed down the text of the Hebrew Bible, that God used them in his providence to preserve and protect his divine message. Yes, I know that's theology, so I won't go further than that.
As for analyzing the verses to "second guess" the Masoretes, one of the best ways to prepare students for that in my view is to use immersion or semi-immersion methods so that students learn to appreciate Hebrew as Hebrew. To learn to think in Hebrew, to read Hebrew with comprehension. Not to focus on parsing and translation, as BH courses typically do. I have not personally used Buth's materials so I can't speak to how Biblical his Hebrew is. But his approach to it as far as method goes is the right way to go. The more traditional way, the more common way, teaches students more about Hebrew than actually teaching them Hebrew. Not to say that other methods or approaches have no value, but that if we are serious about teaching Hebrew as a language, then use methods that have been proven to actually produce language acquisition.
Over the last few years, I've gradually retrofitted my Hebrew studies to include living language approaches. Still a work in progress, but it has helped me a lot when reading the Tanakh. One project I plan to get back to soon is to try this approach to learning Hebrew vocabulary, starting with Jonah. Instead of just providing English glosses and parsing data, I would provide the vocabulary with definitions written in Biblical Hebrew. This is an experiment, and I don't know yet how it will go. I worked on it awhile back and got the first draft of 1:1-5 done. Later this year I plan to get back to it. This data would be incorporated into a slideshow format with images and hopefully sound files. Again, an immersion or semi-immersion approach. If it does come to fruition, I would value your feedback to improve it.
P.S. I am also adding notes on Greek pronunciation and Latin pronunciation to the Resources page at the appropriate points.