It depends on the camera I'm using. With my Olympus E-M1 Mk2, which has a sensor readout speed of around 1/60, it's fast enough that I can use the electronic shutter for most things. I only switch to the mechanical shutter (which operates in a electronic first-curtain mode most of the type, changing to full mechanical above certain shutter speeds) if I'm shooting something that is very fast, or occasionally when there's fluorescent lighting and I'm worried about banding. I've read on Sony forums that people worry about electronic shutter impacts on bokeh, but I don't know the specifics about it. I haven't noticed any difference between mechanical and electronic shutter, though. Otherwise, I appreciate the silent shooting in so many ways. It saves on wear and tear for the mechanical shutter. It doesn't wake my young children up when I do sleeping baby photos, and at family parties it's great for candid photos. People can't easily tell whether I'm taking video or a photo, so they're initially always on guard and then ease up. Lastly, because I love Olympus' f/1.2 primes and often shoot wide open, being able to expose at 1/32000 means I'm not dealing with overexposure issues in normal lighting.
My other camera is a Fujifilm GFX 50S. It has a sensor readout speed of around 1/4, meaning that even slight motion (such as if shooting handheld) leads to that "jello" effect. Full electronic exposure is essentially useless. Instead, I use electronic first curtain all the time, which switches to full mechanical above certain shutter speeds. It's more responsive than full mechanical in most cases.
The holy grail of mirrorless camera exposures, the global electronic shutter, will make sensor readout speed issues a thing of the past. I suspect once we have that, mechanical shutters will only be included on select cameras.
