Joel's march through the hospital is framed the way it is because it is not meant to be an entertaining, heroic action scene. It's not about us being concerned for Joel's safety or witnessing him be a badass. It's purposefully melancholy and sad as we see Joel's spiral into violence as he conducts a heinous and selfish act of love. We are not expected to cheer anything he does, whether we agree or disagree with him. It's a bad decision, and I believe there's a strong indication that he's trying to save his dead daughter as much as he's trying to save Ellie.The entire scene is magnificent, and it builds to a climax as we see him continue his descent by lying to Ellie, carrying out the horrific deed, and tainting their relationship in the process.