My kids are 12 & 13 and I've given a little thought to this from time to time. I am just so happy with our pediatricians that I don't want to change their doctors. Their office is in the hospital and one or the other is usually in the hospital at all times of the day. If we have an emergency (not life threatening) I will give their office a call or the switchboard who will page them. They've seen us as late as midnight too. If I call with a problem that either of my children is experiencing, they will see them that day no matter how long they have to stay, but mostly they'll squeeze you in sometime during the day if they can. Having them available like they are is peace of mind for us. They are both fantastic doctors for the most part, one could have a little better people skills(dealing with adults, he gets along quite well with the kids), but his qualifications are not in question at all. I think we'll continue with them until a time comes when my children start complaining about feeling uncomfortable there, or possibly when they get a bit older. I see kids of all ages in the waiting room, so for now, we're all still happy with our choice. These doctor's have been my kids doctors since the moment they were born (they are also the hospital pediatricians for the maternity ward) and I just they know my kids history better than another doctor would too. With all the kids they see, they remember them all too and call them out by name if they see them anywhere.
I just don't think we can get all this in a family doctor. I know my doctor doesn't compare to theirs.