I suspect that if it looks like a crowd close to a thousand the police will shut it down - additionally you need to count those who aren't being admitted, because everyone gathering outside of the dude with the clicker (and the dude themselves) will be in close contact as a result of the event.
The clicker is effective for fire code issues (since you want to make sure X people aren't in the building) but for disease related issues you don't want those people gathering anywhere, and now 1000+ people will have been gathering (at various times of the night) just outside the venue because of the event.
This makes me think of airports and terrorism. I remember standing in a crowd of 1000+ people trying to get through security theater at JFK, and thinking "Anyone could just walk a giant suitcase bomb into this crowd".
That not even one follow-up attack like that—assuredly crippling air travel for months, at least, and increasing the cost of it probably permanently, aside from easily killing dozens per occurrence—happened in the months after 9/11 was when I started wondering whether this Al Qaeda thing was half as well-resourced in the US, and half as well-coordinated, as officials were saying at the time.
Sure, I think the limit is too high too. I just don't think there's going to be any exercising of these rules except against absolutely brazen cases of going over limit.
Specifically, ensuring compliance is as easy as proving non-compliance. Unless the cops are there with a clicker, employee with a clicker wins every time.