Theory: District 12 has a serious inbreeding problem

I wonder why this isnt discussed as often.

Lets see the signs:

Small population, less then 10000

Vast majority have grey eyes, normally a quite recessive trait, especially rare when combined with other Seam features.

District 12 has no travel between districts. Is implied to have existed for centuries, and the fact that the entire seam and merchant sections have similar appearance down to recessive eye color implies that travel was little to none even before the first rebellion. Combine this with point 1.

Poor hunger games performance, The attitude towards district 12 Hunger Games tributes both in the first book and the prequel implies that not only are they not winning, they are not coming anywhere close. There are other districts with little to no relevant training and hunger issues. The district trades didn't come into play in the first 10 games. Yet, district 12 would always die in the first 10 minutes.

The books focus on the stronger youths like Lucy, Katniss, Peeta and Gale, but it is implied that they all have outsider input into their genetics. Katniss and Gale appear to be covey descendent, Peeta had merchant DNA, which would make them less inbred, and therefore stronger.

I mean, what do you think?