As someone who works in T4.....your luggage would only have been accepted in the transfer area if it was checked all the way to your final destination and you had enough time between flights. If your connections are tight, say less than 2 hours, I would always take the bags with you to the next terminal. The bags "touch" several different hands.

Those desks do not have any bag tag or boarding card printers (we had them in the past the but the airlines asked that they be removed). Not sure about the EI agents as they are only there when they have a flight and not 8am when LA is there.