It also didn’t look like he was in a fire fight when he ran into the building. At least in that video
He had crashed his vehicle in a ditch - running from where he had shot his grandmother who had called the police - so there’s the time line to her house and then to pursue him.... We don’t know if he crashed his vehicle because he was driving crazy or the police were already in pursuit. These things we’ll know as the investigation unfolds. We do know he was on the run.
Apparently he had on some form of body armor - which indicates, as doees everything else about the shooter, he had plans to shoot up a school. his wasn’t a spur of the moment deal.