The current 3.68MP OLED EVF used in Panasonic GH5, GH9, Sony A9, A7RIII, Fuji H-X1 is a game changer: it is the very first EVF ever on which I felt virtually no eye strain in any situations.
Combining its fast response and the short shutter lag thanks to the absence of the mirror, the total shutter lag can be shorter even than the Nikon D-single-digit camera.
On the other hand, the rolling shutter can still be an annoyance on the cameras with larger sensors, if you often chase fast moving subjects.
The battery life of the mirrorless cameras is, as already discussed, one of the major pain. I've never in need of a second battery for any DSLRs I've ever used, but I haven't been able to live without one for all the mirrorless cameras I've ever used. Thus I have to charge the batteries of mirrorless cameras way more often than those of DSLRs, which is not nice, especially we have to charge the batteries of too many digital gadgets that we (have to) have today.
So far as the Nikon mirrorless camera is concerned, the transition from DSLR would be very tough. It would be easier for Canon to retain the compatibility of the new full-frame mirrorless system with the existing DSLR lenses, thanks to their total lack of the mechanical linkage in the first place and their proprietary dual-pixel sensor that offers phase detect AF. Nikon has started to offer E lenses only just recently, and the live view AF is abysmal even to put it mildly.
On the other hand, the dual function sensor whose patent has been filed by Nikon recently looks very interesting. It offers the rolling shutter mode (better for still images with the mechanical shutter) and the global shutter mode (ideal for the video thanks to the potential lack of the rolling shutter effect). On condition that Nikon should offer at least the competitive AF system, their full frame mirrorless camera seems to be attractive.