3 main easons why spider silk protein (SSP) produced in goat's milk did not work: (you had it basically right but just forgot about the problem of spinning it.)
1) It was a very small percentage of the milk. With goat milk at about $16/gallon it worked out to about $7 or 8 thousand dollars worth of goat's milk to get enough SSP to produce one bullet proof vest. Far too expensive to be practical.
2) and that wasn't even counting the very high cost of extracting such a small amount of protein from a large amount of milk. Milk is a very complex mixture and the extraction would be a multi-stage very expensive process.
3) but the BIG show stopper was that they could not find a decent way to spin the SSP into silk. The best that Nexia ever managed was a silk about 40% of the strength of pure spider silk which happens to be almost exactly the same strength as silkworm silk. So all they had was a stupendously expensive artificial equivalent of silkworm silk. And of course there was no market for that whatsoever which is why Nexia went belly-up.
Kim's critical insight was the realization that getting the SSP gene into silkworms that already spun silk was the answer.
That was a vastly more difficult thing to do than getting the SSP into goat milk. There are innumerable things in milk and getting the gene into any of the locations of proteins expressed in the milk could have worked. Getting the SSP gene where it would be expressed in the silk gland of a worm was a much smaller target. But now, with zinc fingers, KBLB can hit that target as many times, for as many different purposes as it wants to (the "platform worm").
Maybe the reason that the art project mentioned only goat milk as a source of the spider silk was that Dr Randy Lewis gave them the spider silk and he owns the SSP producing goats that Nexia left behind. Or maybe, as already as been noted, it's just that spider silk producing goat's makes better press than worms doing it. IMHO the latter explanation is probably it.
Personally I would rather that bit of publicity NOT be connected to KBLB.