You have to differentiate between countries here when it comes to check-in procedures as well as between if it's practically possible or simply against the rules.

Many countries have the requirement of seeing a passport, sometimes even a visa and scan both in order to submit it to local authorities (China, Russia, India, Thailand etc). I have checked people in here as well but usually try be physically there for check-in myself.

In the U.S. generally nobody cares who checks into the room as long as it's noted somewhere, either in the comments or formally in the reservation as second guest. That's a simple fact.