per the contract of carriage

Subject to applicable laws and regulations, the Passenger must pay the applicable fare whenever UA, on government order, is required to return a Passenger to his/her point of origin or elsewhere due to the Passenger‘s inadmissibility into/or deportation from a country. The fare will be the applicable fare in effect at the time of the original Ticket‘s issuance. Any difference between the applicable fare and the fare paid will be collected from or refunded to the Passenger, as the case may be. UA will apply to the payment of such fares any funds paid by the Passenger for unused carriage or any funds of the Passenger in possession of UA. The fare collected for carriage to the point of refusal of entry or deportation will not be refunded by UA unless the law of such country requires that the fare be refunded.

As to the purpose of checkin, it really doesn't do much, and it didn't do much before. Until you board the plane, you could always leave, and they would not know. Even if you were in the days of paper tickets and handing them over at the counter.

It gets you on lists, and shows your intent to fly. If you don't check in they will at some point believe you are not flying, but if you do they will think you are still flying. You can for example checkin now for a flight tomorrow and show up at the gate sixteen minutes before the flight and expect to still get on. If you don't check in and just show up a half hour before the flight at the airport, they may have given up your seat because you missed the 45 minute cut off.

It also can significantly cut down the time you spend in line at the airport if there's a huge line to check in.