To put it in perspective, the disparity is equivalent to polling 10K americans and extrapolating to all of america (which, for better or for worse, is what most pollsters do).
You can sample less than 2000 people and get 99% accuracy with a 3% margin of error for a population of 325 million. Increasing the sample size to 10k simply reduces the margin of error to 1.29%, hardly worth the extra sampling of 8k people.
Which is not true here, as the GP correctly notes.
[1] Assuming that you're not measuring average age or measuring 'who is at home', but if you want to see, say, the average political opinion of total USA population, which tends to correlate with age.
Furthermore, how do you gather the data needed to correct the polling numbers without being able to accurately poll people in the first place? Seems like a complete chicken-and-egg problem.
Of course, the refrain I often hear is that as long as you pick the RIGHT 1,000 Americans, it's as good as polling all 319 million.
If it's a proper random sample, then it's far better than sampling all 319 million because it's 95% accurate with about a 3% margin of error and vastly cheaper and actually practical; you can't poll 319 million people.
Polling 10,000 Americans would be vast overkill, in any case.