The population of recent immigrants cannot be anywhere near 50% of the total population. A more likely explanation is that a significant number of Americans are thick as mince. I hear the number is very similar in Europe.

No, I'd say its more impacted by America's small town problem. The US is teaming with hundreds of thousands of small little podunk towns that were at their peak during the height of the manufacturing boom at the later half of the 20th century(you can see all the random little pockets of low literacy in each state in your linked map) . They have all gone to shit now since all manufacturing got shipped overseas and now they're only being held together by ignorance and hatred (and also that one Mega Walmart). The majority of these small towns are populated by the same families that were there working the factory's back in the day, no one moves in and very few ever move out. There is no incentive for the states or the federal government to help keep these slowly sinking towns afloat, seeing as their sole purpose for existing has long gone extinct. So because of this, these towns have struggled for decades to keep themselves afloat, they've had to make budgetary cuts over the years and usually the first thing that gets cut is education. So over time the average education level of the town reduces, leading to the whole reading issue.

I've spoken with your native speakers, I trust the source.