Indeed, the United States is unusual in making it hard by requiring a two-step process for eligible voters — that is, registering and then voting. Most world democracies have automatic registration. And nineteenth century United States didn’t have any voter registration at all. It worked just fine, just as having no voter registration works just fine in North Dakota right now.
To do it any other way — to place the burden on the voter — is useful for only one reason: if you want to keep people from voting. That’s it. And it’s effective! Especially among those who move often, which tends to be those who are younger and poorer than those who stay in the same place for longer.
Don’t listen to anyone who gives you any other reason. Voter registration is hard in most states because someone who didn’t want people to vote passed a law. That’s the only reason, and it’s a lousy one in a democracy.