I imagine that most of those applications are very much tied to the calendar — traffic lights and HVAC systems need to behave differently on different days.
Trying to minimize the amount of broken code that's still running in 2038 is a big part of why people are working hard to fix the problem now.
Maybe we could set them to 1907 and remain happy that near-future leap years and weekdays will align perfectly well. At least until 2100 needs to be skipped as a leap year ;)
Unix epoch: the number of seconds passed since 1 January 1970 and storing it as a signed 32-bit binary integer
The minimum representable date turns out to be on 1901 and zero is a valid value (1 January 1970)... I wonder what problems people with that birth date have? Similar to the person named Null, or Bobby Drop Tables?
Trying to minimize the amount of broken code that's still running in 2038 is a big part of why people are working hard to fix the problem now.