If you want better quality, pay more and sacrifice the flexibility of a zoom. Stop with the pedantic arguing. /rant
While I agree that we went a bit OT, it seems you missed the point in any case - the 70-200 II is a zoom with IQ that surpasses 4 L-series primes in it's range (85/1.2, 100/2.8, 135/2, and 200/2.8 ). But enough.
I agree that the IQ differences between the 100-400mm and the 70-200 II + 2x are minor and likely irrelevant for real world use. But IQ isn't the whole story. The 70-200 II has terrific AF, but many people don't know that in addition to reducing max aperture by 1 or 2 stops, a TC also results in slower AF (programmed into the firmware) - 25% slower with a 1.4x and 50% slower with a 2x, and I can certainly notice the latter.
The bottom line is that TCs are best reserved for occasional use, and if you need a particular focal length, you're best served getting a lens that achieves that focal length natively.