Should the United States have to let even legal immigrants in?

As of recently every time I hear about immigration, my initial thought is, “Why? Why should we have to let people in?” It seems to me that the system has been being taken advantage of for a very a long time, which has led to where we are now.

Obviously US citizens should be able to come and go as they please with the proper documentation, but everyone else? What is stopping us from saying, “Nah we’re good. Don’t want ya”, even temporarily?