" In this paper, we propose a solution to the double-spending problem using a peer-to-peer distributed timestamp server to generate computational proof of the chronological order of transactions."
Everything else in Bitcoin is just turning that timestamp server into a practical(ish) system.
In fact, if the time of nodes is not synchronized, it can cause significant problems and vulnerabilities. If time is too fast, the difficulty adjustment algorithm will think it mined too few blocks and decrease the difficulty.
Really, the timestamp field in most PoW systems’ “block” structs (Bitcoin’s, Ethereum’s, etc.) is just defined as “a number that is higher than the one in the parent block, and not so high that when interpreted as a POSIX timestamp it would land 30+ seconds in the future relative to the local node’s time.” So you just need >50% of the nodes to have a ±30s clock sync in order to agree on which blocks are valid for consideration; and even if you don’t have that level of synch, those blocks will still become valid eventually, once they’re old enough that all the nodes do consider them to be in the past. (And most PoW systems keep around near-“future” blocks until they’re valid for just such a case.)