Thanks, this was my suspicion, but at least we know what to expect and be prepared for some hassle, if we go that route. It sounds it is not very common and the processes are not always automated, which is not good.
In the end, a lot of hassle (updating the check-in page for hours, calls late at night and early in the morning) and stress (there were only 3 seats left to buy on the later flight i wanted) for something that's advertised as quite simple.
My concern/suspicion is that the airline may be holding the last few tickets for sale, maybe the last 3 or so, and not releasing them online for the free same day change, so you have to call in and push them to do that. This is just speculation, but consistent with the two data points above. Or, maybe the latter one was a rare glitch.