Why do some emulators need a BIOS dump?
For example Playstation emulators do, but Gameboy and SNES emulators don't.
Most Gameboy and SNES emulators include the BIOS file in their implementations so you don't need to add BIOS dump files as external sources.
BIOS dumps contain intellectual property therefore it is illegal to distribute them without consent from the manufacturer. My guess is that most developers do not want to include any intellectual property in their emulators. It is the same reason why you won't find emulators being distributed with game ROMs.
EDIT
Taking Gameboy Advance as an example, according to "GBA BIOS FAQ":
The original BIOS code is copyrighted by Nintendo, and, for that reason, not included in the no$gba package.
No$gba includes some sort of a BIOS 'clone'. These 'simulated' functions are providing exactly the same return values as the real BIOS, including for undocumented and 'undefined' return values, and are fully compatible with most or all existing GBA software.
Taking Gameboy Classic and Color as an example, according to "Pan Docs" the gameboy BIOS provides the following functionalities:
So, without the BIOS file, gameboy emulators won't perform these functions unless they are programmed in the emulator itself.
Basically if the programmer decides not to add the BIOS file to its emulator, he has two options: either he can allow users to add the BIOS file manually or he can add BIOS behaviour to his emulator.