GPS does not contain your current timezone, like NTP it gives out UTC.
The reason your phone (that's set to use "New York" as a timezone) knows to change the UTC offset from -4 to 05 on the first Sunday of November is because it has received a firmware update at some point since 2006. A standalone device from before 2006 can not know that the spring forward/fall back dates in the US changed, unless it's updated.
Your statement "None of those require firmware updates. It's quite nice to never mess with the clocks and have everything just be correct" seems naive at best.