Why would they do that?"
So that we can determine whether or not the system is secure before we commit to it. Replacing insecure cryptosystems is usually very expensive.
"the system has not been defeated in any meaningful capacity. That is a strong indicator of security."
As far as the Germans knew, Enigma had not be broken in any "meaningful capacity" either. They knew there were weaknesses but they did not believe anyone would go to the lengths required to exploit those weaknesses:
https://en.wikipedia.org/wiki/TICOM
Saying "well it has not been broken yet (as far as we know)!" is not a very good argument for security. Even AES has better arguments for security, based on models and heuristics that took many decades of work to develop.
"This is by far one of the biggest achievements in applied computer science in the last 25 years"
More than CAT scans? More than the Internet? Even if we limit ourselves to cryptography, it is clear that that is untrue. What do you think sees more widespread use: Bitcoin, or Kerberos? What do you think had a wider impact on the world: Bitcoin, or HBO encrypting its satellite feeds (for those who are not familiar, that was a major step toward widespread DRM)?
Bitcoin as an application of cryptography or computer science is not even a blip on the radar of achievement.
Not this talented. And you are aware that it's likely that "Satoshi Nakamoto" was actually a team of programmers, right? You don't get that kind of collaboration with clueless college kids.
>no formal definition of security properties, no formal threat model, analysis that is limited to a specific attack strategy
Why would they do that? Nakamoto wasn't selling the bloody thing, he was sharing the idea. We, the developers, have done this independently after Nakamoto fell off the radar.
>I think the vast majority of Bitcoin users know little about Bitcoin's security properties or what it means for Bitcoin to be "secure."
Maybe in the last year or so, but before that, 90% of the Bitcoin community was well educated on cryptography, and most of the power users still are.
>The fact that a system is popular does not mean that the system is secure
You're leaving something important out; the system is popular and the system has not been defeated in any meaningful capacity. That is a strong indicator of security.
>It is also worth pointing out the Bitcoin is pretty unique in not having a "bank." Most digital cash systems require that currency be issued by an authority of some kind, and seek only to decentralize transactions (i.e. allowing offline transactions).
No kidding! That's the whole motivation behind Bitcoin in the first place.
>Being the only digital cash system without a bank that became popular is not as big of an achievement as you make it seem
Are you shitting me? This is by far one of the biggest achievements in applied computer science in the last 25 years. Do you have any comprehension of the sheer number of previously purely theoretical methodologies leveraged to make Bitcoin happen? I feel like you're kind of dismissing Bitcoin without really completely understanding it.