Reasons for your consideration:
- The primary current meaning of the tilde is "approximately equal to" which is analogous to the definition of money. That is, you could say that money is "approximately equal to" the goods it is traded for.
- [...]
Problem with your proposal: The possible interpretation is too broad. Nobody knows which currency you mean when using "~". This means you could use "~" when describing any (abstract) form of money, but not a specific currency.
That said, I also think that "BTC" and the "B-with-legs"-symbol are already too widespread to be abolished as currency descriptors of Bitcoin.
ya.ya.yo!
That is a problem common to any new symbol/entity relationship. If it were to be used consistently, I think the tilde could come to be recognized as meaning bits or bitcoin.