But I don't follow the basic assumption that the way native speakers become fluent is particularly effective. No matter how much explicit instruction helps, native speakers couldn't learn basic fluency that way, because there's no way to deliver explicit instruction to a baby.
Agreed, but learning grammar before you can even understand the examples used to illustrate a rule is putting the cart before the horse.
On the other hand, once you know a few specific instances, it's helpful to explicitly point out that they're governed by the same rule and give an abstract statement of how the rule works. That way you can check yourself without relying on a teacher to point out your mistakes.
Being shown a few examples is not the same as understanding them. If the first time you see an example of the rule is during the explanation of the rule, you have to deal with too much new information at once. A good explanation should refer mostly to information the learner is already familiar with.
The first time you see an example of the rule, there's no need to explain the rule yet. You can just memorize the example. The same is probably true of the second and third example. Explaining the rule only makes sense once remembering the explanation becomes easier than remembering the set of examples you need to know.
Good textbooks already do exactly this. Show a few examples of particular sentence structure, using vocabulary and syntax at the level of the learner, and then briefly draw attention to a general rule at the end.