Would it make sense to think of Bitcoin as a money or value protocol in a similar way to other protocols for data (TCP/IP), STMP, POP3, etc?
It seems to me that from a technical point of view, these are different things. When you talk about data transfer protocols, you can use them to transfer virtually any data, they only determine the format of their transfer.
You cannot transfer arbitrary money or assets through the bitcoin system. For example, if you want to transfer British Pounds, you first need to find someone willing to exchange their Bitcoins for your British Pounds at the sending location, and then someone else willing to exchange your Bitcoins for their British Pounds at the receiving location. It is impossible to do this automatically only with the functionality embedded in bitcoin.
Thus, bitcoin, of course, allows you to transfer money, but according to certain rules and in fact only bitcoins. Even if we take into account the controversial technology of Ordinals, they also allow you to operate only with certain data, you cannot transfer a random asset with their help.
Yes, I agree that you cannot transfer arbitrary money or assets through the Bitcoin system. The only way one can transfer value through the Bitcoin system is via Bitcoin. Hence my thinking is that Bitcoin is the only truly decentralized internet money protocol, and that transfer of value through this protocol can only occur via Bitcoin, whereby Bitcoin acts as the transfer medium for the protocol, say similar to data packets for TCP/IP.
I also agree that comparing data transfer protocols with the Bitcoin protocol is technically different things. Here my thought is that there hasn't really been any money protocol for the internet until Bitcoin and hence it would be difficult to compare existing data protocols with the Bitcoin protocol.