The gift is still there, it is up to users to accept this gift or prefer less privacy for their own usability preferences. Even for the fiat/bank gateway one can still use mixers, new private key etc. It was\is always about the freedom of choice for the user and not about mandatory anonymity of the system.
Indeed. We can all envisage situations where speed and security actually take preference over privacy and anonymity. As seen in the Changing threats to privacy video I shared above, the key is user choice.
However, Person-to-Person transactions within four walls will always be more private than using the internet.
Consider this, do you actually even need the internet (active) to transact with Bitcoin?
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https://youtu.be/hwohadcUv4AThank you for the time BitcoinFX. The video by the way was not bitcoin related, yet is one of the free ideas of thinkers & visionaries that may appall others while making other free thinkers applaud, pretty much like how bitcoin came to be.
Going back to your reply though, as much as peer-to-peer transactions within four walls may be the securest form of passing information, the necessity of internet connection is pretty much needed.
Bitcoin transactions need confirmation & distribution. I think it would impossible to do that offline. The design was for a peer network to decide that the transaction is legit and pass that information to everyone else and make sure the transaction is recorded on everyone else's ledger.
So i guess we really could not take the internet out of the equation at all.