Although I could see PoW as a possible antispam measure, and it's been done before (prior art Hashcash)
I was super into using hashcash for antiabuse in social stuff pre-bitcoin, but the difference in hashing rate in-browser versus in C even then rendered it somewhat ineffective at anti spam as an abuser could hash 10-100x faster, and the delays on the UX side for legitimate users made it a nonstarter. With GPUs and hashing asics now that gap is even worse.
(FWIW these days the Steem blockchain that holds the steemit content is delegated proof of stake, for block production.)
>If so, how do they solve the problem of people downloading the blockchain being liable for illegal content added by other users?
Divide each file into N shards, make sure every miner has no more than N/2 shards of any file at any point in time. You only 'get' a complete file if you specifically ask for it.
You might if you wanted it to be censorship resistant and cryptographically verifiable: https://steemit.com