Problem is that you can be a carrier for close to 4 weeks and not know it, and one of your coworkers could be one of those who die when they catch it from you. They've just found that the virus can possibly live on hard surfaces for up to 27 days, up from 17 days, that the virus can be spread simply by breathing, not just contact or through coughing, and they've found asymptomatic people contagious for at least 25 days in some cases, in addition to animals catching the virus from one person and potentially be able to spread it to other people.
One contagious worker who shows no symptoms can infect an entire terminal. In this case, just having obviously sick people stay home is not enough. In fact, in ensures a longer period of expanding the spread.