The automatic feeder comment is on the size of the oyster shell pieces. It has nothing to do with whether or not they can eat it or whether it can be mixed with the feed. You can easily set up an automatic feeder to offer the oyster shell on the side. That’s like some automatic chicken feeders can handle mash better and different ones can handle pellets better.
If a hen is laying, it seems to instinctively know it needs the extra calcium and will eat the oyster shell. If the hen is not laying they usually won’t eat the extra calcium, at least not much, if it is offered on the side. If you have a rooster, he doesn’t lay eggs so he doesn’t need extra calcium. The ones that don’t need it may take a bite every now and then but not enough to do harm.
What’s the harm in cramming excess calcium down their throats? What’s the harm in you eating too much calcium? Same thing. It can do internal damage to you or them. How much is too much? How much is too little? That’s the crux of the problem. If you know how much they need, not too little and not too much, go ahead and mix it. They are your chickens, you can mix it anyway if you wish. Personally I offer it on the side and let them make that decision.