You can indeed 'rightfully stash $1B in cash under your mattress' - but almost any other private/public storage mechanism will involve gains/losses which have to be disclosed.
Right, but capital gains tax is calculated based on the profits relative to the currency in which it was bought and sold with. You have to sell the bitcoin or exchange it for another form of recognized currency in order to pay capital gains on it. This is more or less how stocks work as well.
