IDK, we've had "money over IP" with cryptographic signatures for decades already in various financial exchange protocols, with the main difference from Bitcoin being the requirement of pre-existing trust relationships.
However, since the vast majority of people and institutions do have some pre-existing trust relationships, Bitcoin doesn't bring that much to the table, we already had the technology to wire money worldwide.
Writing your own transaction messages and injecting them for execution to whatever banks hold your money is a standard, widely used product of classical banking, not some novelty. Ages old cash management services and accounting system integrations run off of that ability. It's not P2P, but it remains to be seen if P2P by itself is a worthwhile benefit.
You still need an agent in classical banking for that transaction, even if the agent is just the bank's server.
I'm my own agent and an international network is the bank. Classical banking can't compete with that in the long run though I'm sure they'll still be of use.
Can you elaborate why exactly can't that compete in the long run?
I'm sure that there are multiple niche use cases where being your own agent has some benefits and it will certainly be of some use, but it seems that for the mainstream usage it does not, and there are certainly all kinds of practical advantages for some centralization and delegation of tasks to another agent, so it seems quite plausible to me that the classical banking might dominate the majority of transactions forever.
However, since the vast majority of people and institutions do have some pre-existing trust relationships, Bitcoin doesn't bring that much to the table, we already had the technology to wire money worldwide.