>Isn't your bank balance in a bank database also "just a number"?

Absolutely not, but also "yes, which means no". In the first case, a bank balance isn't "just" a number, it's a massively regulated and legally backed number with many layers of interlocking entities, both private and multiple layers of government, in charge of maintenance, auditing, insuring, and enforcing. There is no equivalency to cryptocurrency there, as has been regularly touted.

To the second, it could certainly be argued that a bank balance is indeed "just a number" and that's the point, what gives the number its value is all the infrastructure around it not anything intrinsic to the number itself. If someone finds out my bank balance in Account ABC is $42076 that might have privacy implications sure, but knowing that number gives you access to absolutely nothing of meaning. That's a completely different situation to one where independently finding a given number, which note you need not even have any idea who it belongs to, suddenly equates to ability to make use of that number in real world relevant ways by social consensus.

We're talking more the equivalent of Adam guessing a winning lottery ticket, and then hanging onto it hoping the value will go up and he can trade on the ticket or do other things with it while not actually cashing it in because it's so unlikely somebody else will guess the ticket. Maybe because the lotto ticket winners are published on a public ledger, and Adam doesn't want the notoriety, or at least not just yet. Then Bob does independently guess it, immediately turns it in, and now Adam's lotto ticket is worthless. Bob didn't steal anything from Adam. Whether what Bob did is ok or not depends on the rules of the game.

>I understand that the bank's ownership of its computer means that hacking into it could be seen as (for example) a trespass

Holy shit are you for real? COULD be seen? Yes hacking into a bank would absolutely mean felony prosecution on multiple counts if you were caught.

>However, what if you somehow persuaded a bank employee to change someone's balance?

They would be committing multiple felonies and you would be committing criminal conspiracy, inducement and so on depending on jurisdiction, and probably wire fraud and a bunch of other stuff if you do it remotely that are sorta gimmes for prosecutors.

>The bank employee has some kind of authority to do this and the result is once again "just a number".

The bank employee does not have legal authority to do this. Any technical authority they have is only within the auspices of the law, internal compliance controls and practices and on and on.

Anyway without going through your whole post you're doing a whole lot of false equivalency. Breaking into and modifying somebody else's systems is no small point, it's explicitly illegal under the CFA in the US and similar in the rest of the developed world. There's no such thing as legally "copying" money from an end owner perspective, even if internally to the global financial systems when it comes to fiat currencies from the Treasury & Fed or other national equivalents to banks and other governments and so on it gets more complicated. It's all meant to effectively be a digital version of actual old fashioned hard currency. Hence the entire core concept of theft: it applies to zero sum games, where one person getting more cash means another person now has less.

I'd welcome any actual specific laws on the books about cryptocurrency that contemplates what would happen if someone simply guesses a private key with no interaction with anyone else and then uses it on the network. But without that it's hard to see any existing precedent. On the contrary, cryptocurrency people have repeatedly pushed, and built into the core foundations, the notion of code being law, that possession of a private key is all that's needed and the rest is up to the network and you're supposed to be in charge of that (or someone else is on your behalf and that relationship can be subject to contracts).

>Cryptocurrency gains are taxable in many (most?) countries.

So?

>Clearly the governments see cryptocurrency as something more than just random numbers without meaning.

Not really? It's the realized gains that get taxed. That's a completely generic feature of the tax system, the government doesn't give a shit (and shouldn't) what people decide has value in any given transaction. The only thing they care about is whether or not there was actual cash equivalent value exchange happening. Barter is always a potentially taxable event. The government makes no judgement on whether you do it with pretty river rocks or random numbers, they can assess the value of the exchange as if it was done with cash and tax that result.

Re: Seizure of everything related to an illegal operation: sure, they will take everything they can find regardless. They'd take a computer with a ~/.ssh full of random keys too. The data they seize might also have pirated movies/games/music. Some of the things might have "value" but that doesn't make them currency.

None of this implies the result you clearly wish it did.

>Is the government agency just going to throw its hands in the air and say “oh well, he guessed the random number, nothing more we can do!” No, I think not.

You "think not"? Why not? What laws do you think are being violated? There are lots of cases where the government will seize something that might at the time of the seizure be worth $X, and then legitimate activity happens elsewhere such that now it's worth $0.5X or whatever, and that's perfectly fine. The question hinges on whether the activities of other independent people/entities unrelated to the criminal entity that got seized are legitimate or not. It's not a matter of vibes. Like, imagine the government seizes a winning lotto ticket. And then before they can do anything with it somebody unconnected else goes into a convenience store and legitimately buys a ticket, guessing the number too. The value of what the government seized has just dropped. Would I expect the government to throw its hands in the air and say “oh well, he guessed the random number, nothing more we can do!”

Well, yes? That is indeed my expectation, within the rules of the game in question. If the lotto says "if you fail to claim your winning ticket within 1 week before someone else guesses it as well then too bad" or "well then you both split it 50/50" or whatever, yeah I'd expect the government to be held to the exact same standard as anyone else.

You might be surprised how many crypto hackers have been arrested and convicted. Usually they want to spend the money in civilization.