Routine instead of "schedule"

So as a breastfeeding mom, as I was told to "feed on demand". When Lincoln was a newborn, if he wasn't sleeping, he was eating. Now that he is older (4 months), he does more. Some places say to establish a schedule for your baby. It's on the notes at the pediatrician's office, Lincoln's school has one, there are books like Baby Wise that talk about the importance of a schedule. I still do not feed by a clock. At school, the teachers will ask, "He eats every 3 hours?" My response, "We do not follow a schedule, we follow his cues." So that is why I say we have a routine. We eat, play, sleep. There is not a certain time or duration we do these things every day. When he wakes up at 6:00am on weekdays (because we have to get ready for school), I feed him. Once he gets to school, he plays for as long as he wants. He'll let you know he is finished by rubbing his eyes, sucking his fingers and lying his head down, whining, etc. We rarely let him get to a cry. We pick him up, swaddle him, place him in his crib or swing with his pacifier. He sleeps as long as he wants. He'll grunt and let out a few screams to let us know he is awake. We pick him up and start all over again. Some days he plays longer than others and sleeps longer. We start winding down at 7:15-7:30pm with a story and bath and in bed by 8:00pm. It gives Joe and I two hours of quality-time before we go to bed ourselves. I feel like it is an easy routine to follow and we're listening to Lincoln's needs at the same time.