He did, several times. Infact Arthur coughed and touched alot people before even chapter 6. It's actually a miracle and unrealistic no one else in the camp got sick with it. He shared drinks, food and tobbaco with people, got his TB bacteria over everything he touched and coughed on. I'm going to say the main reason would be, would you rather be able to riddle Micah with bullets, or have him slowly die off screen?