I still shoot primarily on DSLR. I don't know how a modern mirrorless compares, but for me shutter lag is the big killer when it comes to action shots.

I grew up shooting 35mm film and my first digital cameras were a shock with their significant shutter lag. To some extent I can "learn" the lag for a given camera and compensate somewhat for things that move regularly. For irregular motion (like sports) shutter lag is maddening.

Re: hopeless - I supposed you could use multi-shot burst on laggy cameras and pull the trigger early.

Modern digital cameras have a mode where they are constantly taking pictures in a small rolling buffer and when you press the "shutter" button it simply keeps the last n seconds of images. It is an amazing feature for action photography and is how a LOT of amazing shots have been captured.

With 6k and higher res video the line between video and photography is blurring and with RAW codecs you can just capture scenes in video and pic out what frames you like.