I think you may have misunderstood something here.
When paying for Claude Max even at $200/month there are limits - you have a limit to the number of tokens you can use per five hour period, and if you run out of that you may have to wait an hour for the reset.
You COULD instead use an API key and avoid that limit and reset, but that would end up costing you significantly more since the $200/month plan represents such a big discount on API costs.
As-of a few weeks ago there's a third option: pay for the $200/month plan but allow it to charge you extra for tokens when you reach those limits. That gives you the discount but means your work isn't interrupted.
Extra Usage for Paid Claude Plans: https://support.claude.com/en/articles/12429409-extra-usage-...