The trait may or may not be advantageous. Diversity is. In this case the selective pressure is poaching, but selective pressures are constant. Diversity is a bank of genetics that the population can draw from to adapt and survive.
Traits that are rare, are often rare because of shortcomings. But if environmental changes make that tradeoff worthwhile, it can be made. Meanwhile, evolution doesn't stop. Once the trait/gene is common there is positive selective pressure on complementary genes. Over time, these may mitigate or compensate for the negative traits that have acquired.
Of course, on the timescales that humans tend to selectively pressure species, there isn't time for all this elegance to emerge, usually.
Yes, but in the long run isn't this breeding out this specific diversity? I recall reading that genetic diversity becoming limited in endangered species makes them much more susceptible to being wiped out by disease.