The question is why would large, centralised entities use a blockchain to settle between each other? Large, centralised entities generally can and do trust each other to the extent required, so won't ever need a blockchain because they can use a more efficient system...

It may unfortunately be path-dependent, and the large entities that exist now will not choose to convert. However, if you imagine a parallel universe in which blockchain was invented before large institutions formed, then those institutions may have formed around Blockchains, because then they wouldn't have to trust each other.

Right now, getting into the 'trusted financial institution' list is extremely difficult. It's a slow, incremental process that takes decades of good behavior and careful stewardship. Part of the reason it's so difficult and so heavily regulated is because of how much trust we place in these institutions. If we did not have to trust them so much, it would be easier to become one. It would have less need for regulation. Incumbents would be weaker, and the industry as a whole would therefore be healthier. This is sort of an abstract point, but I think it's the truest sense in which blockchain may change the world: by commoditizing trust.

it would be really cool to be able to verify the ownership of any property on earth by checking Bitcoin or Eth block chain, but there would have to be a way to have authority unanimously change the record.

Beyond curiosity, what practical purpose would such a tool serve vs other methods of verifying assets?

by signing with a keypair you could prove to anyone online you owned something. to list a house or get a loan or mortgage you could use this.

a really neat case for this would be lost items. if each cellphone had its IMEI and your keypair associated you could prove you owned something lost. or if found someone could look you up to return it. you could buy a game or software once and never have to worry about a serial key.

You can do this now, by having centralized state based repository with API. Estonia might have something like this already.

I haven't worried about serial keys in years. Didn't need blockchain for that.

So how many copies of this enormous blockchain would there be in the world?

Perhaps a solution to that might be to give the government the authority to relabel a token. That is, every property is represented by a unique transferable token. However, the ledger that says which token represents which property is maintained by the government, centrally. Under ordinary circumstances, this ledger is not consulted/used but when say, someone has their property seized by a court, it might be.