The magical world probably is also inherently bad at scientific process. They don't have any higher education that we know of, their numbers are very low, and their longer lifespan probably leads to higher levels of institutional conservatism than in real world. Even the one research department we do know of doesn't seem have much peer review process with the whole "unspeakable" thing.

Science is the collaborative effort of millions of researchers, the magical worlds just doesn't have the numbers or the institutions. However, magic does allow for a higher proportion of amateur scientists, which is pretty much how it worked in the 17th and 18th century.

I'd say lack of peer review is the biggest shortcoming for magical "science". A schoolkid was able to come up with improvements for potions in the textbook, but twenty years later no corrections have been made and the same outdated instructions are repeated over and over again.

 

First, I really think the whole "magic vs science" debate is inconsequential and trivial to debate. However, I do disagree with the whole idea that "science cannot be applied to magic". Most of what we know about magic theories, rules, etc. come from Harry's POV, and he's not the most academic one. So we could be missing out on a lot. Secondly, there's no denying that magic do have a mostly consistent effect, that can be measured and test. We know that there are Unspeakables, who seem to operate like researchers and scientists to a degree. Of course, it's reasonable to assume that wizards do not have a rigorous form of scientific theory (I like to imagine that it's more akin to a natural philosophy).

When Psychology first began, there was a whole lot of pseudo-science guessing going around. Simply because the mind was far too abstract a subject. We knew that certain things and effects happen, but it was still murky. I imagine magical theories are like that. Magic being an abstract and mysterious, although controllable, energy.

 

The only person who can answer this question is god... aka Rowling. You wanna apply science to magic? Go ahead. It will involve creating and interpreting a whole system which is consistent with how canon magic works with a lot of technicalities thrown in. If one is willing to put that much work on the world building you're better off writing an original fic where magic and science aren't mutually exclusive like in canon but rather complimentary to each other.

 

Well, magic certainly seems to take precedence, no doubt, but I wouldn't say it operates entirely outside the mundane world either. Magic is able to subvert reality and natural law, yes, but for that to happen they must be able to interact, and we have things like magical plants and animals. They are, and seem to remain, intimately intertwined. That's why magic is "genetic." Magically genetic, yes, but still bound up in that mundane human process.

So while Muggle sciences might not help so much with any mechanical or immediately applicable form of magic, I think a more minute study of what the natural world is and what its laws are without the influence of magic would shed, perhaps, some light on just what it is that their magic is doing, and maybe a bit of how it works, by what mechanism it influences nature, and so forth.