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@peterscheen out-of-the-box Zuora computes a charge line item for usage even if there is no usage reported (even if the total figure comes out to $0).
There are a few options here: If you are not reporting any usage during a period then there is a Zuora admin setting called 'Do not process usage charges without usage records'. This has to be enabled by Zuora support with the PM's approval, so you could open a case and discuss your use case to see if this might help you.
The other option if you simply want to hide these charges from the user's invoice PDF, would be to hide the rows that are $0 for usage. We do something similar for our quotes but the concept can be applied to Invoices as well. I wrote a guide on how we did conditional rows for Quotes that you could look at for reference, and I am happy to answer any questions you have on it: