IN SOME WAYS YES IT IS WORTH THAT 6,000$ PRICE TAG. My justification is all dependent on my style of shooting and wanting less impact on the animals photograph.
My style of shooting is quite different when I shoot with the 600mm lens compared to when I shoot with the 70-200 is II L + 2x III converter. When shooting with the 600mm (bazooka) I position myself in a blind or ether down game trails where there are signs of animal activity. Then well to put it quite frankly I wait for something to happen and this can take hours or even days.
The 70-200 f2.8 is II L + 2x III converter is so much lighter than the 600mm and is easily handheld making it more portable and allows me to venture out in the brush and look for action. I usually take this set up while exploring locations to later bring the 600mm.
Overall its up to you on what style of shooting you have, Weather or not you are willing to spend the countless hours in the brush to get that killer capture. Or be mobile and keep looking for that next amazing image. All that matters in end is that you capture the image and both setups are easily capable or doing so.