Why do mirrorless cameras still have mechanical shutters?

Just got my first mirrorless camera a Fuji XE-2. I've been liking it so far. One thing is noticed is the viewfinder blackout seems longer than my Nikon DSLR. I take it this is because the shutter has to close first and open again to get the exposure since it's previewing off the sensor. A traditional DSLR uses an optical viewfinder to preview so the shutter would have already been closed. I've noticed some mirrorless cameras have the option to use an electronic shutter for silent or fast burst captures. So why is there a need for a mechanical shutter at all?