Quite right. The 28-300 most emphatically is NOT "pro" glass. I use my 28-300 when I'm in the a situation where I need that much focal length on the long end but haven't the foggiest idea how close-in I'll have to work, and it's a situation where I can't carry alternative lenses. Rarely happens. But I'd prefer to take the 24-120, which is far superior to the 28-300, Ken Rockwell to the contrary notwithstanding. The 28-300 jumps to f/5.6 before you've zoomed very far, and that's a long way from your preferred f/2.8.
Never knew about a Nikon 20-400 f/4, and I can't seem to find it listed anywhere. Strikes me that if there were such a beast the compromises would make it something like the "zooms" that were around in the sixties.