I think it's not possible to do ethically or practically, because only some sorts of people will willingly subject themselves to the testing, examination and prodding of of social sciences, even when bribed. And if you tried to force it on them using a government, which would be unethical, you still have the practical problem of the data you get from people under duress being garbage.

Probably just requires a bigger budget than most academics have. I got paid £50 to spend half an hour giving feedback on a new website, in a 1:1 conversation with a researcher. Granted the funding was from government, but Kantar did the organisation side.

No, all you need to do is hire a professional polling company. They also have biases but they're far closer to providing representative samples than MT is. Academia doesn't do this because it's expensive and they have a cultural bias towards quantity over quality.

There are many companies that specialize on this. Usually, it takes picking random people at many different streets, but does not require government intervention.