Mixing brands bothers you? Curious, personally I could care less about that. How can you avoid that in building a PC?
I imagine most of the motivation for staying within one brand for a case and fans, is the manufacture should know what works best, and the components are optimized for the specific situation. That is logical, but assumes that each fan included with the case was designed specifically for the case, which is not a given. The goal or purpose of a PC case design has a large influence on the fans, is it a case for maximum component cooling, or for minimum noise. All fans trade the amount of air moved vs noise, since the perfect fan (silent, with high CFM and static pressure) does not exist.
I have an NZXT Phantom case, and its NZXT 200mm fans (two max speed versions available) are designed specifically for it. Fortunately, those fans perform well in both noise and cooling (when their speed is controlled) so they stay in the case.
I also have a Corsair 500R case, that has a different 200mm fan. IMO, that fan is terrible, worthless in its application. That fan was replaced with one of the new 140mm Corsair fans, which is far superior. The other Corsair fans that came with the case are quiet but not great for cooling, so they are gone.
The point of all this is, whatever works better to achieve a goal is what I use. I change the fans in a new case over and over until I come closest to my goal. That might be all, some, or none of the original fans in the case, plus possibly additional fans. The Phantom case has three of the four original fans removed, with another NZXT fan added, and two other different make fans. The 500R has all of its original fans removed, and has four different makes of fans now.
All of the PCs I've built are a combination of parts from different manufactures, which IMO is just what works the best for me. I'm blind to a brand's name, focused only on the result.