Wouldnt it be easier

Yes, it would be much easier. But that's not the goal.

What does this accomplish

The people who are drawing the line here, with suspicionless stops at an "internal" border checkpoint (which is just made-up bureaucratic nonsense since "internal" and "border" are supposed to be mutually exclusive concepts) may be the ones to help stop this kind of mission creep.

The border patrol has already crept inland up to 100 miles. There are numerous interior checkpoints and no one is disputing that. So then we must ask, where will they go next? Maybe the borders of each state? Cue the next wave of people invoking their rights at the state borders and the other wave of people, people like you, asking "What's the big deal? You just answer a question and keep moving." Sure, that's probably true. But then after a few years of being set up on the state borders, Border Patrol decides to go to every county line with the same questions. Cue the same two types of people. Then Border Patrol is at every major highway junction, checking papers. Then at every stop light. Then every neighborhood entrance, and by that time everyone would be thinking, "how could this have happened?"

Am I saying that's what WILL happen? No, it's somewhat far-fetched. But is it theoretically possible? Abso-fucking-lutely, and it has actually happened in other countries throughout history.

What if instead of asking what country you're a citizen of, they asked what color underwear you are wearing? Would that be intrusive enough for you to not like the idea of answering? What if they asked you how much money you make? How many people you've slept with? It's none of their business, and neither is your citizenship. Some people, like you, don't find that particular question intrusive, but maybe this post will help you see why some people do.