I'm super fascinated by the entire concept of proof of work and how it allows for a trustless, decentralized system. Despite knowing that proof of work (or proof of stake) can be an inevitable necessity to having a cryptocurrency like Bitcoin, I'd like to fully understand where other methods fail.
The first problem Bitcoin addresses from my understanding is signatures with each transaction. To me, this completely makes sense, as it is completely necessary to be able to verify that the sender indeed was the creator of the transaction. But then the next problem is transaction order and validity to prevent double spending. I don't understand completely why a timestamp can't just be included for every broadcasted transaction, and the transaction could have the correct, universally agreed upon time, and each ledger gets sorted chronologically. Is this because it requires a centralized system to prevent people from forging timestamps? Or what am I missing? To me, it seems like if the transactions were broadcast publicly to the entire network, there wouldn't be conflicts in ledgers / double spending.
And how exactly does the main blockchain stay decentralized? Let's say I go offline and miss transaction broadcasts, and now I want an updated version of the main blockchain. I would have to rely/trust others for this main blockchain, which seemingly is centralized now in the way that all new users are pulling from this same copy of the blockchain. I don't quite see how that's different from the analogy with a community ledger with everyone just keeping their copy updated with that, or a main branch on a git repo which everyone continually pulls from. There is no single point of failure, but it seems to still be a community ledger in a sense.
I am completely well aware that the "solutions" I presented above have faults somewhere that I'm missing / scenarios in which these will fail which I haven't considered, and I'd like to understand exactly why a proof of work system is necessary in these scenarios. And, how it can stay decentralized and trustless despite having characteristics described in the above paragraph. This, I believe, will help me understand the true beauty of it.