So what's so great about mirrorless then? Is it just about size?
The biggest benefit is to the manufacturers, is they are cheaper and easier to make and they can be sold with higher profit margins. The cost savings are not passed on to consumers.
Size is the smallest benefit, and not really true. The shorter flange distance could maker a narrower body, but you could do that anyway and just have the mount protrude. The real limiting factor on size is the lens-mount diameter, sensor size and IS packaging, and most of all ergonomics. Tony camera bodies with huge lenses are just stupid. The hand grips need to stay the same size to maintain the same comfort.
And if you make the flange height smaller then most lenses have to be made longer to accommodate, e.g. a 100mm lens needs the font element 100mm form the sensor, if you move the mount 20mm clsoer to the sensor then the lens needs to be 20mm longer. You see a lot of Sony mirrorless lenses are both longer and heavier than Canon and Nikon DSLR equivalents.
You do save about 150grams form losing the mirror, but it seems with the massive reduction in battery life you will loose all that weight and more in batteries. Even the latest Sony A7/9 camera have terrible battery life compared to a DSLR., because the sensor has top be powered the whole time.
With no mechanical moving parts reliability increases. Shutters typically had a 300,000 life span, but could be replaced at cost. Even for a pro it would eb rare to use a camera so long that the mirror mechanism wares out, so this gain is probably pretty minimal to most. On the flip side since the sensor has to get powered up the whole time, and a complex EVF, there is the increased possibility of electronics failure.
Mirror-less cameras can silent shoot, if they taker care of a mechanical shutter noise which some earlier Sony bodies didn't
Similarly, with no mirror slap there can be less vibration, but I think it was one of the early Sony high res bodies taht had terrible shutter slap, far worse than the mirrorslap of a D850 for example.
The AF overall is worse because the PDAF sensor have to be far smaller. This is especially true for continuous shooting. The D850 and D5 are far better than even the Sony A9. There are things that mirroless can do better at, for example there is no issues wit focus misalignment, and the sensor can be used for things like face detection AF. These things can actually exist on a DSLR in live-view mode
The EVF has great potential to allow better manual focus, assistance, exposure verification etc. I don;lt think the technology is quite there yet.
The biggest gain for users is perhaps continuous shooting speed, pro cameras top out at about 12FPS due to the need to flip the mirror to focus. Hard to imagine flipping the mirror up and down much faster. Given sufficient processing power, you could have a mirror-less run at 20-30FPS. For sports and wildlife this could be a huge gain, but currently we are limited by processing grunt and the cameras would gridn to a halt.
Mirrorless is the future, but there is no overwhelmingly critical improvement. There are pros and cons with all current mirrorless cameras, and so it depends what you shoot if the pros outweigh the cons.