I agree, but I think it's potentially confusing to say the GPU should output "limited color range". Unless the TV doesn't support it, the GPU should output RGB 0-255, the PC default. As I understand it, the only alternative is for it to compress everything to 16-235, either as RGB or YCbCr. For this to work for video, video must first be expanded to RGB 0-255, causing the dreaded levels round trip of 16-235 to 0-255 to 16-235. I'm going to assume below the card is outputting RGB 0-255, which means it can pass through whatever is presented to it.
As for the video player and TV, the main consideration is, do you want consistency between desktop and video? If so, the video player should expand Video Levels to PC Levels, i.e. 16-235 to 0-255, and the TV should be set to PC Levels ("Non-standard" for my ST60). For video, this discards BTB and WTW and scales all the values in between into 0-255, which is necessary for Black = 0 and White = 255 to work for video as well as the desktop. If you don't care about this, then your video player can leave the video untouched and output Video Levels, and your TV should be set accordingly ("Standard" for my ST60). This is the WMC default and Kodi's "Use limited range" option. This is passthrough for video and preserves BTB and WTW, but the TV will crush black and probably at least some white on the desktop, as it should be calibrated for Black = 16 and White = 235 (overshoots allowed). This is not a problem unless you use the PC for gaming, critical picture viewing, and whatnot. It won't interfere in the least with using WMC or Kodi, nor will it interfere with maintaining the PC and even writing letters and such. This choice provides consistency with video devices like streamers, BD players, etc, some of which may not have RGB 0-255 output options, e.g. my Sony S5100 BD player only has RGB 16-235 (however, unlike a PC, it doesn't appear to do a levels round trip). This consistency would let you hook everything up to an AVR and use a single AVR HDMI output.
Agree completely with using the TV for all calibration. I use the second of the two approaches just above, and my PC and BD player measure the same under the same calibration, which is all done with the TV. This was not the case when I had the video player output PC Levels; then, I had to make some tweaks to Brightness in the Nvidia Control Panel to get Bar 17 to show up in AVS HD 709 Black Clipping.