Similarly, automated check-in kiosks are then usually unable to find the reservation via credit-card or passport scan -- meaning you're back to looking up the reservation code, and even that often fails, as if the apostrophe just flat-out causes issues with the query/lookup or something.
It can be very frustrating, and I'm increasingly often impressed (and vocalize the same) when I spell my name and the agent enters it correctly AND the system flawlessly handles it, too! The DMV systems in my state are one such example where I used to have issues but, in recent years, the problem appears to have been wholly addressed/handled.
That being said last time I went to the US the person booking the ticket swapped my first name and last name. Only the person at the baggage dropoff noticed it, and after much deliberation they suggested to leave it that way. I went through with no issues apart from not being able to register the mileage.