With Cardano's ambition of bringing self-sovereign digital identity and finance to billions of people, it is important to consider that many people do not have constant electricity or stable internet.
Right now, running a Daedalus full wallet takes several GBs of storage and will take quite a few minutes to hours to synchronize the blockchain even with a decent internet connection, so this probably won't be an option in that situation. But even with a light wallet like Yoroi for Android, it takes a while to check your balance.
In a situation where you have two people with a smartphone with a Cardano wallet on it that want to transact together, what is the minimal internet traffic and time needed to send funds from one phone, and get final confirmation on the other? Would it matter if the phones are on the same local network?