Science

That's a good point about disease and I think it could be a potential cause of the low genetic prevalence.

I don't know about your roaming free option. I think if that were true, there would still be wild packs today or there would have been roving dog packs mentioned in historical text (possible but I don't recall any mention of them). Alternatively, they would have inter-breed with European varieties and had a more significant impact on genetics, but that's not seen.

While I agree that Europeans liked to remove/exterminate "uncivilized" things, that mostly applies to people. I suspect if the American dogs were significantly useful they would have made use of them.

This conversation allowed me to recall that the plains tribes utilized dogs as pack animals. Then once horses made their way onto the scene those tribes switched from dogs to horses for that role. I'm not sure what other "jobs" American dogs performed but I suspect if they were significantly utilized as pack animals they were probably breed for such and with that niche gone they may not have performed well in other "dog" tasks, compared to European varieties.

To conclude, for American dogs to be such a small percent of the current dog genome, I think, the European varieties had to significantly outlive their American counterparts. Whether because they were replaced by better performing European varieties/horses, because they died from European diseases, or a combination of those options.