Look at gears... You will see kernel.bin only contains game data. No executables. Kernel .bin is the same in both the PC and PSX cersion. the PC version has kenerl2.bin, but that's just sections of the text sections in keneral.bin (Part 10 and on) in LZSS format.
The kernel is responsable for the following.
1) Communictaion to the lower BIOS and PsyQ API.
2) Ownership it's own higher-level game API. (Play music, load model, user input)
3) System Memory Management
4) Thread managemant.
5) Loading and unloading of modules.
....along some ohther things, these were the big ones.