Further, getting anything less than As closes doors for that child in the future - permanently.
That's a complete myth.
No, it's actually somewhat true, but that doesn't mean any of those doors are necessary desirable destinations, or that getting less than A's in a class is a barrier to any actual measures of success (e.g., happiness, status, high-paying job, etc), or the opportunity cost of working towards that A results in a overall better life.
Of course, although there are very few consequence for lower GPAs in early schools, there are actual consequences for a pattern of mediocre grades as you advance in schooling (putting students in "tracks" is nearly inevitable regardless of your schooling options) which does pin you into certain corners of future outcomes.
At least in the USA, it's possible (and perhaps even not uncommon) to break out of the consequences of "tracks", however, in many countries in the world, it's nearly impossible to do so, so it is not exactly a "myth".
We'd like to think there should always be a second chance at a door, but often in life there are usually not. However, most of the time, there are often many alternatives, some of which may be even better than the original choice, but this isn't the same as a second chance at a door, and you need to learn to identify these situations and catch that door before it closes, if it's something you really want. If you need to teach your kid anything, that's probably the thing to teach them.
Similarly, the opportunity cost of working for something as abstract as all A's, might be too high a cost to pay relative to other uses of someone's time (say spending the time learning/practicing some valuable "hobby" that would be valuable in the future, or on interpersonal relationships). As someone who used to spend time working with college admissions officers, I'd say this is the unspoken reality of the college application game that parents often fail to understand: A's can only get you so far...