Timely post, as those are the 3 lenses I currently own. Recently re-added the 100-400 to the lineup for its MFD powers. The 600PF is my primary lens for birding, it's going to take 90% of my photos, while that other 10% is for when a situation or species requires me to be able to shoot close-up below the 13' MFD of my 600PF. The 400 4.5 is giving me an additional ~5' of space to shoot, but the 100-400 grants ~10' and a metric-ton more focal length flexibility. The loss of 2/3 stop of light and tiny bit more sharpness do not factor into my decision making, as I feel the flexibility and MFD of the zoom far outweigh those tiny advantages for my use case. Additionally, earlier this year I auditioned the Z 105 MC, but ended up passing on it because I just don't do enough macro to justify it, but now with the 100-400 I have both a birding lens but also a pseudo-macro when I get the itch.
So why do I still have the 400 4.5? Truthfully, I just haven't been able to work up the fortitude to sell it yet because it's such an amazing little lens. The intention was to pair it with my (long since sold) 800PF, and then my 600PF, for the same closer-MFD purpose, plus the 1-stop aperture advantage for shooting in shaded, woody areas or on overcast days. It also would make for a fun, minimalist travel setup w/ the 1.4TC, but I haven't been able to convince myself to do that yet because I like the 600PF too much to leave it at home
There's also an esoteric reason as well: I prefer the simplicity of a prime over a zoom, that limitation breeds creativity. I like going out with an intention to make a photo working with constraints, taking just the 400 4.5 to see what I can do with it.