You don't need to trust everyone to hold to hashrate limitations, you have a closed network, you just need the majority of participants on the network to agree kick out any violators.
Here's an article describing how the majority of hashrate was reversed once for Bitcoin itself:
https://bitcoinmagazine.com/articles/bitcoin-network-shaken-...
The largest miners all agreed to switch to the 0.7 chain, even though the 0.8 chain had more CPU power. This could just as well have been done on a closed bank network by e.g. everyone agreeing that Deutsche Bank are being dicks and trying to take over the network, and simply manually ignoring what they're mining.
If you're one of 10 miners on a closed network and you know the other 9 will simply start ignoring you if you break the rules, you don't have any incentive to break the rules.
You also haven't come up with any plausible scenario for why one bank would even bother to do this. If you're using a private blockchain for e.g. a SWIFT replacement as discussed in this thread, what's Deutsche Bank going to do once they become dicks and acquire 99.9% of the mining power? Disproportionately pay for running the whole thing? They don't have any interest either in screwing up the network or approving double-spending or whatever, since they're also using this SWIFT-replacement just like everyone else is.
Claiming that this is "useless" in "a world with off-site replication of databases" is missing the point. You're just failing to imagine that there can be anything on the spectrum betweeen a 100% centralized system with 100% trust and a 100% decentralized system with 0% trust.
How is a group of 10 banks who needs a SWIFT-like system going to run a traditional DB with off-site replicas, say the primary fails, which replica run by the 10 banks does everyone agree to fail over to? You'll very quickly just need some centralized party to run the whole thing at a large cost, and you'll end up with SWIFT again.
This is the part that a private blockchain makes easy. You have banks or other private parties that all benefit from running a low-cost distributed ledger, they can firewall this off from the open internet, and all of them just have an interest in keeping the system going as-is at a low cost.
It's easy to monitor whether some party is breaking the basic rules of mining, and once you have that setup adding new banks becomes a much easier lower-trust operation than e.g. giving some random new bank read-write access to your traditional RDBMs SWIFT replacement.