* Transaction throughput.
* Efficiency - allowing small scale players to participate in verification and block production.
* Inter-chain communication - some networks are explicitly designed as connected swarms of chains (Cosmos and polkadot for example) and some evolving into that direction outside of the protocol level (Ethereum). How do execute transactions that span the networks is an ongoing research topic.
* Privacy - how to execute transactions in private. How to attest that something is true, say that you have a certain credential, without exposing your account information. Blockchain has been why zero knowledge (and now homo-morphic encryption it seems) cryptography are becoming an active field of research.
* Identity, authentication, account recovery. - these tie into cryptography but generally research on applied cryptography with good UX. For example the first time I've seen social-recovery accounts with any amount of usage (now a feature in Apple accounts) was in a blockchain application.
* Monetary research - far from everybody involved in crypto believes that a fixed-supply rare item makes for good money. "Fiat" money is basically a "token" with governance attached to it. This has lead to a wave of experimentation with other forms of tokens - ones that are algorithmically tied to other assets, ones that are backed by an organization, local currencies, etc.
* Organizational research - since smart contracts can effectively be transparent community banks there's has been a plethora of experiments with building organizations that manage their own treasuries. Horizontalism, organizational transparency and cooperation is something that's been at the core of many crypto projects, the idea being that something cannot be both a reliable public good and controlled by a single party. It's not an easy task, but some cool organizations have come out of this. For an example look at pocket: https://messari.io/report/governor-note-proof-of-participati...
If you think about it you are very limited in what you can do. You have an asset that you can self-custody, exchange permissionlessly and without censorship which is good to fight what the original article is about. But you cannot build any financial product on top of it that would have those same properties. Nor be able to scale the transactions per second that the base layer does while keeping those same properties. And I find it very unlikely you can serve the entire world with 7 transactions per second. So yes, there is plenty to innovate on its core function.
Correct, and yet you seem to still miss the point. There are tradeoffs. You can't scale AND maintain those properties. This is why Bitcoin scales with layer 2 solutions like Lightning (and more ideas like Enigma, Ark, Cashu etc.), or things like RGB or Taro for expressiveness. Separation of concerns.
The best attempts to have their cake and eat it too have failed in crypto.
There is very little innovation to be had in the core function of what a blockchain was designed to achieve. There's plenty of innovation ahead of us for the layers that are built on top of it.
zk-proofs allow you to do so. It's seeing very active development, and yes it involves an L2. The issue you seemed to have ignored is that to be able for the L2s to inherit those properties from the L1, the L1 needs to have sufficient expressiveness to be able to build the proof verifiers. I would love to see how anyone builds such a thing on bitcoin.
