“Lets the user set the correct timezone” is where this falls down. The user doesn’t always get this right. Once that happens, the time looks correct for a while, then looks wrong all of a sudden. So they go into their settings and manually change the time. At that point taking time from the network provider no longer happens, because they overrode that.
The predictability of DST doesn’t help, and “most people never have to adjust their timezone” isn’t relevant either. Perhaps you didn’t fully grasp what was happening in the example? All of the machinery works correctly, it’s just the first time they set up the computer the timezone was wrong, or they moved. Everything after that point can work correctly, but if that thing is wrong, UNIX time will be wrong even if the time looks right to the user.
I’ve literally had to fix this problem for people. “Correct” time, incorrect timezone. It’s not a theoretical example.