Employing PoW to protect against Sybil attack in anonymous network is the very invention that made Bitcoin possible.
Without PoW you must ID participants, which makes system trivial to regulate or shutdown (see Facebook Libra, or security fraud case against Ripple). And no, PoS isn't the answer, because PoS implies a handful of biggest exchanges control the coin, because they genuinly stake the most.
If Bitcoin was PoS, Mt Gox would run Bitcoin to this day!
- Signed transactions being broadcast onto a p2p network
- This network being visible to anyone who is interested
The much less important part of crypto is exactly how the shared ledger is assembled. So long as these transactions are put together in a relatively timely manner, and no transactions are being willfully excluded, whatever mechanism used for assembling the ledger doesn't really matter that much. Proof of work is literally just a time-gated lottery for some entity to be the one that gets to say "I am submitting the next update to the ledger." They're not providing any service to the network that a single shitty chromebook couldn't provide on its own, the time-gated proof of work is literally just to arrive at a consensus. There are so many alternatives that make more sense than this.
No! It is of *critical* importance how the shared ledger is assembled, because Bitcoin's threat model assumes the World's governments descending upon the shit, eventually!
The blockchain assembly with proof of work, while an interesting and very creative solution, is just one of a multitude of ways you can arrive at a consensus.