See the other commenter/thread that recommended I do this. I'm worried that by doing a chargeback, I will be blacklisted from using Anthropic's services, which I feel like is a reasonable assumption.
Until they do start doing identity verification, I think you're good. Frankly, don't be a coward. If you're getting treated like this, why would you even want to use their services in the future?
If the product is really so good that you're willing to let the vendor abuse and defraud you then just treat it as a cost of doing business and move on. Personally I wouldn't tolerate that, but I guess it's a matter of priorities.