Cases are lower still or zero in many other places with far too few cases to have achieved herd immunity. The only plausible explanation is that containment measures have some effect.
But in any case, the immunity level of the population reduces the need for other measures in order to stay below an R0 of 1.
There’s a massive spectrum of efficacy in the dozens of different suppression or containment policies that can be applied, combined with demographics and geography of the location being studied.
But in any case, the immunity level of the population is a downward force on R0 that, for example, will naturally keep daily cases lower in New York vs. Florida regardless of policy.
The case rate has dropped faster as the restrictions have eased.