The beginning photographer learns quickly that the self-timer is very handy to avoid touching the camera when the remote shutter release is not available. The remote shutter release is still useful for situations where timing is critical e.g. fireworks but one can never forget to bring along the built-in self-timer. ;)
However, things become a little bit more complicated when dealing with DSLR. DSLR has a mirror which also causes vibration and hence most DSLRs have a mode called MUP for mirror lock-up to reduce camera shake. For obvious reason mirrorless camera does not have the same issue.
Can the photographer combine both self-timer and MUP? It is not possible on my Nikon D610 as the self-timer and MUP are separate items on the mode dial. I heard that it's possible on Canon though.
However, there's a workaround -- by using the Exposure Delay menu option (d10). This introduces a delay of up to 3s after the mirror goes up. So I can turn the mode dial to self-timer mode and set the timer to be, say, 2s. Once I press the shutter release, the timer will countdown 2s and the mirror will flip up. After 3s then the shutter will open and the picture taken. The 3s exposure delay will hopefully negate any vibration caused by the mirror flipping up.
Last but not least, according to http://www.photographyblog.com/reviews/nikon_d750_review/ this workaround also works on the Nikon D750.