Claims from JWT only get you so far as you pointed out, and can quickly lead to token bloat.
In a 'perfect' scenario, if a user is interacting with a resource, the handling service will be the one most likely 'owning' that data so will be pulling it out of the database anyway - and so can pass it along to the PDP. If the PDP was also going out to fetch state, then that would be two separate systems querying for data rather than one.
I appreciate that isn't always the case depending on your architecture, but we see the benefits of the PDP being stateless and a known quantity interms of how it handles data being a reasonable tradeoff.
If you would like we can jump on a call and go into your specific use case?