Mike
I don't know what kind of aeronautical GPS you use, but your description does not match the way mine works.
So there I am flying along, and I decide I want to route direct to DETling.
I hit GOTO DET and a large pink line pops up on the screen from my current position to DETling.
I could hold my current heading and not turn towards DETling, and the line will not follow me. Rather, the line will stay where it was, and I will deviate from it. This is common functionality amongst the Garmins; less so amongst the cheaper more generic GPSes.
If I wish to fly a constant track towards DETling, I just follow the original line. I normally have "track up" on the map, making this very easy. If the track line is perfectly vertical and the little aeroplane is on the track, I know that I am holding off exactly the correct drift.
Tell me where I am wrong...
Charlie.
It occurs to me that I should have added.
Most fixed GPS installations in aircraft are also connected to the HSI or VOR CDI Indicator.
When you hit GOTO, the needle of the HSI/CDI is initially centred. If you fail to track correctly towards the target you leave the Track line, and your HSI/CDI shows a deviation.
If the installation were to work the way you describe it, the HSI would always be centred.
Charlie.