Of course it won't be over kill, its just how much u are willing to spent on FX lens
like a 50mm f1.8 i don't think its a over kill for D300.
Like a 70-200mm, as long you are happy with the IQ, overkill does not matter.
The 70-200 VR1 is invented when Nikon did not have FX digital camera yet. The infact the lens was optimized for DX cameras at the time. Therefore it is the best bet for your D300.
Long before DX lenses with the smaller image circle appeared on the market, Nikon was producing lenses to accomodate the 36 x 24mm (FX on D3 & D700 and Kodak DCS14N) format 35mm film cameras. Some good some bad.
DSLR with smaller imaging sensor is just a progression of photographic imaging technology.
Why is there an overkill? Do you know that for most of the lens, the sweetest spot is around the center of the lens? Therefore, when using 70-200 lens on an DX sensor, most of the image will be sharp.