I don't know any American adult who doesn't have a government issued ID. You basically can't do anything without one.

I imagine that for many Americans, they don't have a government issued id

That's only the case in a few select cities, like New York. Most other people have an ID of some sort. (And, even if you don't want a driver's license, it's still possible to get a government-issued ID that doesn't let you drive but still verifies your identity.) The US is huge. It takes at least a few days to travel across it. And most of it, especially out in the Midwest, is still pretty rural.

As for the "two forms of ID", they actually require four types of documents (though some documents can be submitted for two or more of those things; at minimum, you need two documents total), at least in my state, when you first get a driver's license. So most places will simply use your driver's license by itself since it proves that you've already proven your identity. Anywhere that does require two proofs will usually use your social security card and your driver's license.

IDs are super common in America, it would be unusual for someone to not have one.