BDEMU (the payload) is not needed to play backups, it's needed to grant access to the Blu-ray emulation of the PS3, and to redirect dev_bdvd to "PS3 GAMES" menu on the XMB.
You need a disc in the drive to launch the game on the disc icon.
BDEMU is also used to emulated and mount the external USB drive as a Blu-ray drive. (BD mirror)
BDEMU OR Lv2 Patcher are needed for that (this is the payload which allow access to system calls).
BDEMU is a permanant solution (installed in the multiMAN folder, and loaded automatically by multiMAN), while Lv2 patcher needs to be launched by the user before using multiMAN, and is kept in memory until you switch off your console. Choose only 1 method, don't launch Lv2 patcher before using multiMAN if you have BDEMU installed.
Gaia and Rogero already include the payload, so they don't need lv2.
but if you are using a custom firmware with a payload, it can cause conflict. If the user want to use PL3 payload instead of Hermes, etc. it's not possible if the payload in forced into the manager, so Dean removed any sort of payload, and let the user choose the solution he wants.
Installing an older version of multiMAN doesn't create a bdemu.bin file, the payload is included in the eboot.bin.
The BDemu-Kmeaw.pkg and BDEMU-Wutangrza.pkg (signed) install exactly the same file (bdemu.bin) in multiMAN/USRDIR/ folder, there are 2 different packages because one is signed for wutangrza while one is not fir Kmeaw cfw.
BDEMU has not been removed because of Sony, but because it allows Blu-ray emulation and BDMV file copy to internal HDD for mounting later without the original Blu-ray Movie. It's considered as "DRM protection circumvention device" in some countries.