Yes, Bitcoin solves BGP (in some way). It solves also a bunch of other completely unknown problems:
* how to prove some information existed at a certain time
Incorrect. It only proves some information existed at a certain block. There is no way to
put[objectively prove] a clock time in the block chain.
* how to create a public ledger of ownership
Incorrect. A longest-chain-rule (LCR) block chain records non-conflicting state transformations. That isn't limited to a ledger of ownership.
* how to issue a currency without requiring a nation state army to enforce scarcity
Incorrect. A block chain can distribute tokens. That doesn't guarantee anything about it becoming a currency and being immune to nation state armies. If not immune (i.e. not defensible against), then 'without' is incorrect. (it doesn't even guarantee the distribution won't be centralized by mining farms)
* how to reach agreement over a communications channel on value
Again you are pigeon-holing what a block chain does. Again a longest-chain-rule (LCR) block chain records non-conflicting state transformations.
E.g. last year there has been 1B$ investment in this area, and there been almost no progress at all in terms of advanced applications (just an increase in noise levels).
Thanks for ignoring my progress and thereby insinuating my sharing/progress has been noise.
I think the possibilities are largely not explored.
I appear to be reasonably skilled at distilling to the generative essence and I will assert that there isn't a large space of possible designs that will work to eliminate the centralization issue. Mine seems to be the only possible one.
Now that is noise or at least veering very far from a solution to the problem this thread raises.