It sounds like you have a fairly small run, otherwise you would not be removing poop from it daily. I agree with everyone else. Chickens peck at the ground and eat things from the ground, even each other’s poop. That’s how they share probiotics and develop flock immunities, eating each other’s poop. That by itself is not a bad thing, I consider sharing probiotics and developing flock immunities a good thing. I want my chickens to develop a strong immune system, not try to keep them in a sterile environment.
The risk comes in when the poop load gets too high, especially if it gets wet. If it gets wet it will probably stink plus if it is wet that is a breeding ground for some diseases. Wet is your biggest enemy, but the heavier the poop load in the ground the higher the risk. I never clean poop out of my run but mine have a lot of room so the poop gets really spread out. In my coop I use a droppings board and do not crowd my chickens either. The heavier your chicken density the harder you need to work especially on poop management.
There is a rule of thumb to not feed any more treats than they can clean up in 15 to 20 minutes each day. That way they maintain a balanced diet since their main feed is a balanced diet and it stays the main portion of what they eat. I don’t follow that, especially when going through the waste from my garden, but I do want them to clean it all up that day. I don’t want to attract vermin or predators plus I don’t want it to go sour or moldy. I do toss it on the ground, not in a container.
Chickens eat dirt. They get grit from that, they get minerals and other nutrients from that. It helps keep them healthy. As long as you are feeding treats in moderation, toss them on the ground, depending of course on what it is. I’d feed yogurt in a container. As a bonus, they will scratch and help turn your ground, helping it dry out of it gets wet and spreading the poop you miss so it’s not as concentrated.
