I find that the parents that want to drop in and have multiple visits before care starts that it has nothing to do with the child and is all about the parent's issues. That is something they are going to have to come to grips with and me and my daycare children are not going to help them do it at our expense.
After I tell them about the drop in anytime and then leave with your child rule I also remind them that if they begin to abuse the privilege that it will be grounds for dismissal because I have an obligation to the other children to provide a consistent day. That can't happen when children are constantly coming and going, our storytime or craft time is being constantly disrupted.
When I remind parents that if I let them drop in 2-3 times in the week I also have to let the other families drop in that many times and that is a lot of coming and going. And well yes it is generally the newest family that wants to do the drop ins there will come a time when their child has been in care for awhile and I am interviewing other new families for a space in my daycare and then it will be their child that will have to endure the constant disruptions and often there is a lightbulb kind of moment for the new family realizing what I allow them to do now they will have to live through down the road too and don't like that prospect. They then understand why I have my 10 minute - ie say hi, dress your child and go home rule.