I don’t believe there is such a requirement. I suppose it depends how deep of an integration you’re imagining. At the no-tech level you can simply have crypto backed redeemable notes - like the old gold standard.

There are also things like M Pesa/MobileMoney which have half a billion users in sub Saharan Africa. Simply an account balance held by telcos, accessible from any GSM phone. It’s custodial but could easily swap in crypto and extend to the rest of the network if there was a movement to do so.

But even without all that, vanilla crypto transactions don’t really take much bandwidth. You do need a connection of some sort but just running a light client is not very demanding by any means.