My friends argue about the best strategies for this. Will send to them to stoke the fires.
Once you persist it - you might as well be using a session. I suppose it depends on your scale - maybe with just a couple of thousand users it would work ok to store every JWT issued for their lifespan.
I agree that persisting the JWT means you may as well be using a session, but my takeaway from that is that you should just use a session, not come up with more weird workarounds to justify JWTs.
If at scale this option doesn't work - or at least not as well as you'd like, additional strategies are good to know.
If you plan for Pokemon Go, or Fornite scale, decoupling may be beneficial. Admittedly this is a small percentage of all of the use cases.