Your familiarity with the system didn't do you any faovr this time around. Even for the simplest domestic flights you should not assume you would be able to check in online until you've actually checked in online. A number of issues (say flight being oversold, lack of available seats to the online system so requires airport seat assignment or maybe even just system outtage) could have prevented you from checking in online.
The VA
online check-in website clearly says you are unable to check-in for "international travel" not just international flight. It seems like you are just assuming you would be able to check-in online for the domestic segment without actually checking what's supported and what not. It even specifically recommended if you are connecting to an international flight from a domestic flight you should check in at the airport at least 90 minutes before the domestic flight depature time. Additionally, the
Contract of Carriage was worded such that VA provides no guarantee for the availablility of online check-in service, and still requires you to arrive 30 minutes prior to depature.
It's not uncommon for online check-in to simply fail if the ticket involve an interline connection (VA-SG interline in this case). I've personally experienced this many times when flying between the US and AU back in the days when VA and DL were friends on an interline ticket. VA and SG likely have agreements in place to have VA verify travel documents and check you in to the SG flights and tag your baggage through so an VA agent at the airport needs to physically check your passport.
Sounds like the agent still helped you out here. I don't understand why that would be unsympethetic. The system automatically transfers the flight to gate control past 30 minutes so dispatch can start working the numbers on loading the aircraft and the gate to start working through any seat change required for balance and any stand-by travel. No check-in agent have the authority to check you in, unless an operations manager approves the revert of gate control and it would certainly mean the flight will be delayed as those dispatch work have to be redone. The ironly should be clear if you just picture youself sitting on the aircraft unable to go because one passgener was late checking in.
Contract of Carraige again specifcied that VA is entitled to move you to the next available flight, or simple treat you as a now show and cancel the whole thing.