YOu can imagine a situation where R0 < 1, but only due to a strategy that includes some methods that only work when the absolute number of infected people is low. Something like fighting fires in California brush: everything’s flammable, potentially you could have a big fire, but as long as you run around quickly putting out little fires ( before they spread) you can prevent it. But if there are too many little fires, the one-armed paperhanger effect kicks in and things get out of control.
In such a metastable situation, controlling the number of visitors could be important.
Now if R0 is well under 1.0, and that is all due to strategies that have no problem scaling up, a few infected visitors is an annoyance but not a big threat.