The Sony 300mm f2.8 GM is a relatively popular lens. It's light enough for hand holding (at least much moreso than the 400mm). From what I've read it works great with the 1.4x teleconvertor and still holds up well with the 2x TC, giving you a much lighter 600mm than the 200-600mm and of course way lighter than the 600mm f4. It's a long way past "inexpensive", but it's still thousands less than the 400mm f2.8 and 600mm f4. IMO the real competition for the 300mm f2.8 is the Sigma 500mm f5.6, which is an incredible lens for the price, but has the typical Sony limitations of 15fps and no TC.
I think Canon would do well to offer something like this as well. The 100-300mm is an incredible feat of engineering, but it's a chonk. Or take a page out of Nikon and Sigma's book and make hand holdable "affordable" primes like the 500mm f5.6 or the Nikkor 400mm f4.5 and 600mm f6.3.