What I've found is some types of screen time in the morning don't interfere with my kids getting ready for school, but other types HAVE been a problem, so I have banned SOME types of screen time on an as needed basis. Here is where things stand right now.
12 year old, No basement family room TV time before school. When we allowed this, she just got lazy and falls back asleep or doesn't get anything ready until the last minute, then she is almost late, panicing and forgetting things. Watching some PBS in the kitchen or while eating breakfast, OK. No Netfix anytime during the school week. No Wii on school mornings. No cell phone until she is 100% ready to walk out the door for school, including all her things she needs in her backpack, teeth brushed, socks and shoes on, glasses on, breakfast eaten.
9 year old, PBS on in the ktichen/dining room while she is making or eating her breakfast has been OK. No netflix anytime during the school week. No using my personal laptop in the morning, so no Webkinz, no Club Penguin. No Wii games either. When she is 100% ready to walk out the door, she can have her Ipod Touch (this is usually only about 10-15 minutes) but only for games, not shows. And it does not go to school, ever.
My kids are generally pretty good about my rules because if they know if they behave they can watch Netflix kids shows on Fri and/or Sat night. If they have a fit, they have that privilege removed.