If all bitcoin is mined, I think the problem would be the transaction time and fees
Actually not, once segwit and lightning network fully implemented there will be lesser fee and probably faster transaction as well. And of course, core developers will keep upgrading the software/codes without opposing the vision of Satoshi.
On the positive side, If bitcoin would be fully adopted (which is hard to happen), there would be scarcity of btc which would make it more valuable than before.
Once it happened, as per the law of supply and demands goes, even miners get only little by little fraction of block rewards until btc fully mined and only rely from transaction fees, it still enough for them. As for that time, approximately 2140, bitcoin value might be 6 digits or even more.
So it all depends on the adaption of users to crypto, especially in bitcoin.