I just joined this forum to report this same issue. I built a new PC: Asus Crosshair VIII Dark Hero, Ryzen 5900x, Asus 6900 XT Strix, 32GB TridentZ 3600Mhz RAM, Sound Blaster AE-9, Seagate Firecuda 530, and a Corsair H150i Elite Capellix to which I added three LL120 fans from my previous build added to the radiator for a push/pull configuration, all inside an Obsidian 500D SE RGB from my previous build. I am also using two Corsair branded RGB strips. They were on the other side of the case and I had forgotten about them. I moved them to the top and front of the inside of the case by the mobo and radiator, and connected them to the 12v aRGB header. So other than the RAM, all RGB is Asus or Corsair. All fans are connected to the Commander Core. The previous build had two corsair RGB nodes and a Commander pro, but I removed them for this build.
I am using the latest iCUE, and the latest Armoury Crate. All of my Asus RGB components start up with the RGB settings set in Armoury Crate. However, the Corsair fans and the strips do not load with settings. The strips are through Crate, but are doing the same thing as the fans. I have to do what OP does to get my iCUE profile loaded. I also have to run Armoury Crate to get the Corsair led strips to sync up with the Asus Aura settings. My previous build was working fine, with my iCUE profile loading up when I booted into Windows. So it seems to be an issue with the latest version of ICUE and Corsair RGB components. It is annoying to have to boot up both programs to get the Corsair components to load the chosen RGB settings.