The radar will draw a green route line from the aircraft to the destination along with the entered route when the departure and arrival airport has been added to the flight strip. However when the departure airport is missing no green route line will be drawn. In multiplayer I always add an fake departure airport in the flight strip just to see where the aircraft should be going to. Therefore, the green line should be drawn even when the departure airport is not set.
Reproduce with:
Start SOLO game with APP mode and 1 initial traffic.
Select aircraft and see the green route line to the airport.
Edit the flight strip and remove the departure airport.
Save and close the flight strip.
Now the route line is missing, even though the arrival airport is still known.
Not exactly a bug, since a single destination detail does not define a valid route. It may be a little theoretical, but it is impossible to have a consistent system if we draw a route while only knowing the destination. One reason it can become dodgy to try and draw everything in the case you present is, for example: define departure AD, exit point and destination (like it is automatically done in solo mode if you have exit points defined). Then do as you say (remove the departure). At this moment there is a likely chance that your exit point is ambiguous.
So I understand the disappointment, but in the end I tend to see this more as feature than as a bug as you can detect an invalid route by not seeing it drawn when you would expect it to be. In real life you would normally NOT know destination without departure. Even VFR pilots should inform of both---as far as I have seen but is this ICAO requirements or could this be different in certain countries?
Moreover, if a valid AD is filled as destination, ATC-pie does recognise and display it in the second line of the radar tag with a direct heading to it from the radar contact position.