https://www.wolframalpha.com/input/?i=plot+%281-%280.999%29%...
At around the 700 mark, the probability is > 0.5. So if you are in a crowd of 700+ people, someone's likely sick. Of course, you need to have some reasonable estimate of how many are carrying the virus in a given population to do this calculation.
Not counting the 2 outdoor amphitheatres, I can name 8 theatres in my area with capacity >1000. Several more in the 800-999 range, and I'm not sure if these thresholds would apply to "audience in the house" or "total souls in the building".
Seattle's gathering limit is much lower (250) than SF's, and includes "social distancing" and other limitations, which essentially shuts down all concerts, plays, musicals, conventions, and lectures.
For example, I see the 5th Avenue Theatre here (capacity: 2100) just cancelled their entire run of a show that opens this Friday (8 performances/week for 3 weeks). That would have potentially been >50,000 people.
I estimate bans like this will prevent the intermingling of at least several hundred thousand people each month, in each metropolitan area which enacts it. I'm no expert on the spread of disease but that seems pretty significant.
It's not only the fact that it's a large number of people gathering, but also that it's a large number of people in close proximity to people they wouldn't otherwise be from out of town who are at higher risk of having been exposed to the virus. They pass it on to a few people at the event, who in turn take it home and give it to family members and in a few weeks the city has a big problem.
Obviously this is the simplest possible way to look at it, not modeling how many of those people actually come in contact with one another, the probability of transmission, etc.