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Bitcoin is digital property, and you use it like cash. If you don't like the term wallet, than call it a money clip? I agree it technically isn't accurate in regard to what is happening under the hood but from an abstract user-experience perspective, there is no better analogy than wallet. This is true of lightning and on-chain.
Technically bitcoin doesent actually exist in the wallet at all, but in the blockchain because "your coin" is a public ledger entry that can only be modified by signing a change authorization with your private key.
Keys aren't a good term for asymmetric cryptography either, because the full analogy should include the lock too. Keys and locks aren't exactly correct either, because you aren't using it to open a thing but to scramble data. A smartphone isn't technically accurate because the phone part is technically just the microphone that measures sound, and there's not much smart about that part. Telephone isn't accurate either because it leaves out the electric part and the reciever/speaker part. The same applies to the words phone and speaker, terms drawn from poor analogies.
You can critique almost every word built on an analogy used in the world and find them lacking, but the reason we use them is to convey their usefulness to people who don't care about the intricacies under the hood.
I say we stop mincing words and let the inventor of a technology have the right to coin words around it. To do otherwise simply seems rude and cheeky.