Wandmakers are few, and have individual techniques
The magical world is not like the modern one. There are only a handful of wandmakers, and only one who is any good:
“But wands — what’ll people do for wands?”
“They’ll make do with other
makers,” said Lupin. “But Ollivander was the best, and if the other
side have got him it’s not so good for us.”
Harry Potter and the Half-Blood Prince
Garrick Ollivander, for example, was the one who decided to use only certain cores in his wand production:
Early in my career, as I watched my wandmaker father wrestling with
substandard wand core materials such as kelpie hair, I conceived the
ambition to discover the finest cores and to work only with those when
my time came to take over the family business. This I have done. After
much experimentation and research, I concluded that only three
substances produce wands of the quality to which I am happy to give
the illustrious name of Ollivander: unicorn hair, dragon heartstring
and phoenix feather.
Other wandmakers have other techniques, and may well be secretive about them, particularly when it comes to sharing them with scorned groups (such as goblins). It is this last point, I think, that Griphook references: it would seem that no wandmaker to date was been willing to share sufficient details of wandmaking with goblins to enable them to make a working wand, and it is difficult to attribute this to anything but widespread prejudice.
As for figuring out how to build a wand given the finished product….
Compare this to say, the real-world task of building a emulator for the 3DS. It took years from the the release of the 3DS to get to a stage where the best working emulators could barely play modern games. Now imagine if the secret of building a 3DS had been developed and passed down in only a few families. We’re dealing with a far smaller scale here than modern industrial production.
I’m not aware of any evidence of non-human magic users successfully creating a wand in canon, though.
It’s also not totally clear that the details of wandlore can easily be “reverse-engineered” from a stolen wand, and, even if they could be, the results would likely be far less than a wandmaker such as Ollivander, with all his tricks of the trade, could accomplish. For example, goblins also keep their secrets of magical metal-working from witches and wizards, and I am not aware of any wizards successfully reproducing, say, goblin-made silver.
But the main obstacle is legal
It’s not impossible that a goblin might successfully create a wand (though, without the knowledge imparted by a wandmaking family, it would probably not be quite as good as it could be). The problem is that such a process would probably be illegal. We know that no non-human can use a wand:
“Here, look.” Mr. Diggory held up a wand and showed it to Mr. Weasley.
“Had it in her hand. So that’s clause three of the Code of Wand Use
broken, for a start. No non-human creature is permitted to carry or
use a wand.”
Harry Potter and the Goblet of Fire
It is highly likely that it is also illegal for a non-human to attempt to make a wand, or for a human wandmaker to share the details of wandlore with a goblin or other magical being. In other words, the the refusal to “share the secrets of wandlore” is likely codified into law, which would add to the reluctance of goblin to try to make a wand, or a human wizard or witch to share secrets about wand-making.
As a side note, even in the modern world, there are secrets of engineering that are successfully kept secret from the majority of people (besides the previously-mentioned proprietary systems, such as the 3DS). For example, this answer suggests that the principles behind building a thermonuclear weapon are at least partly secret (an ordinary atomic bomb, though, is a apparently trivial).