I just encountered this yesterday in a drive from Memphis, TN (Central) to NC (Eastern). The initial ETA was based on Memphis time. When I crossed the time zone boundary and the time reset on my phone, the ETA updated to the real ETA of the destination time zone.
I don't know why it would be difficult for Waze to know the destination time zone and display the correct ETA based on the destination time zone, not just when the device enters the destination time zone.
For the user that commutes from Knoxville to Nashville, I would expect your ETA would change accordingly too, once you enter the Central time zone. So what would the difference be if it shows the destination ETA from the beginning?
Basically, you can't share the ETA (accurately) until you cross the destination time zone boundary. IMO, the ETA should always be based on the destination time zone.
I have 3 NAV apps on my Galaxy S4: Waze, Maps, and Here. Of those, only Here provides the correct arrival time using the destination time zone. But it displays the drive as being an hour longer than either Waze or Maps. Go figure.
OnePlus 3 on AT&T