Is blockchain efficient or should we drop that from the tag description?

A public, permissionless proof-of-work blockchain is inefficient by design. It's a feature, not a bug. That inefficiency is what makes is secure and solves the double spending problem. It is the inefficiency which requires at least 51% of the entire network's CPU power to hack it. So a real blockchain has to be inefficient and that is what makes it unsuitable for real world usage at scale.

Private, permissioned blockchain is more efficient because it doesn't use proof-of-work. But that's kind of pointless. Blockchain was supposed to be decentralized. Private blockchain violates the central tenet. If it is controlled by a central authority, why even bother using a blockchain, just use a regular database.

Depends on 'which' blockchain. Clearly both Bitcoin and Ethereum are overhyped blockchains and have proven to still be inefficient in what they are designed to do.