I got the 100-400mm II last year and have used it a lot... Love it! But I still keep and use 70-200mm (actually two of them, f/4 IS and f/2.8 IS).... And I keep and use 300mm f/4 IS (two of those, too... one probably headed in for repair after about 10 years).... As well as a 300/2.8 IS and a couple other long lenses.
There are times when I have to use the 300mm f/4 or 70-200mm f/2.8 due to lighting conditions. I try to use the 100-400mm II as much as possible for it's versatility and quality... but there are times that f5-f/5.6 just won't cut it and I need to use the faster lenses along with a high ISO (6400) and a just-barely-fast-enough shutter speed. With my 7DIIs I can and sometimes do use even higher ISOs, but that always means more post-processing work and fairly limited enlargeablity/croppability of the finished images.
Plus, a high ISO setting doesn't do anything about AF performance. While the 100-400mm II has reasonably fast and highly consistent AF, in good conditions I think it's just a tiny bit less fast than either 70-200, 300/4 or 300/2.8... but in more challenging/marginal lighting conditions it slows just a little more, isn't as "instantaneous" as the larger aperture lenses. Shooting a lot of sporting events and fast action, I need AF to be as fast as possible.
I've at times used the 100-400mm in place of 70-200mm and thought I might be able to live without those shorter zooms... so long as light was reasonably good and/or that last little bit of AF performance wasn't necessary. But, I don't want to imply that it's not fast focusing. It is. In reasonably good light it's fully capable of locking onto and tracking fast moving subjects:
And it's versatile zoom range let's you catch the subject farther away or much closer, too...
But, the 100-400 II weighs in at about 3.5 lbs. That can be a factor if hiking with it or on extended shoots (above was on a tripod... during a 4-day state championship event with close to 12 hours of near-continuous shooting per day... 17,000 images total). The 70-200/4 weighs 1.7 lb; 300/4 weighs 2.6 lb; the original 100-400 weighs just a tad over 3 lb.; and a 70-200/2.8 comes in at 3.25 lb. The 100-400 lenses are also larger diameter... hand holding them for a long time is more tiring than the smaller diameter 70-200s or 300/4. The increased weight of the 100-400 II is probably due to it's robustness. The guys at Lensrentals.com love to take stuff apart to see how what's inside and they called the 100-400 II "the best built zoom they'd ever seen". So, the slight increase in weight is a trade-off for more durability and reliability.
Also, the 300mm and 70-200s are all IF/IZ lenses... "internal focusing/internal zooming". They don't change length and shift balance when focused and/or zoomed. On the the other hand, the 100-400mm is not IZ... it extends quite a bit when zoomed. While this upsets the equilibrium slightly, it doesn't prevent using the lens on a gimbal (as was the case with the above series).
Sorry... but image quality of a 70-200 + 2X combo is nowhere close to that of either 100-400mm, and especially the II, used without a teleconverter. Even the best EF 70-200/2.8 IS "II" with the most ideal EF 2X "III" falls a bit short. Any other combo of lens and 2X makes for a bigger hit on IQ and will not be able to equal the 100-400s.
Gene51 is correct, too... with their apertures (which are necessary to keep the lens a reasonable size) the 100-400mm lenses have less ability to blur down backgrounds.
IMO, the 100-400 II is a superb, versatile and highly capable lens. I really like it and use it a lot. But for me it doesn't completely replace some other lenses. But that's just me. Other folks may find it can take the place of one or more other lenses in their kit.