I think if you want everything to be equal you should have all like things. Especially with speakers. Since different companies use different materials. Using multiple different speakers with different materials could change the sound. I'm not saying with Atmos speakers that it would make a huge difference. But if you're going to spend the money on lets say B&W, you might as well just get the remaining speakers to finish the room. I have zero data or charts to back up my suggestion about using the same speakers throughout the build. Haha.
Everyone I've chatted with in stores has always said to "try" and use all the same speakers for a home theater build or music build.
Fair points, and keep in mind I'm not saying it's a bad idea, but that's not really grounds for a firm opinion on it.
I recently built a new system from the cables up, new room, the whole 9. I've dabbled in HT before, but for the most part I've been a 2ch music guy since the 70s. My wife is a movie buff. When I set out to build the new system I said this time I wasn't going to skimp on home theater. I shared the same thought as you on speaker branding.
As I stated, it's never a bad thing to do, but for movies, the side/rear/atmos channels don't have much of a need for tonal balance with the mains...even if a different brand might have a slightly different tone for the same sound effect, it's not discernable, a bullet whizzing by sounds very similar from speaker to speaker.
Multi-ch music I'm finding would be more of a reason to have surround speakers with similar drivers to the mains...some sound engineers send full range signal content to the rear speakers in 5.1 music.