Proof of work is a form of money[0], with extraordinarily unequal distribution[1] in people willing to front the cost of spinning custom single-purpose mining silicon. A social media site that uses proof of work is equivalent to a social media site that is explicitly pay-to-play, where ordinary users will be censored for being too hashcash-poor to participate.
I mean you'd expect that the amount of work you'd have to put in to rank would stay quite low.
You can also combine it w/ traditional social graph techniques to further prevent the work threshold from going past what you can do on a typical mobile phone.
At the very least it seems like it would work to bootstrap discoverabilty before social graphs really start to develop w/ more usership.
The problem is the inequality of specialization. The whole point of proof-of-work is to add costs that are trivial for even the poorest user but add up quickly for someone who wants to sockpuppet, ballot stuff, or otherwise spam the system. This only holds if all users pay relatively the same amount of money for access to compute power. If you can specialize - that is, invest capital into making a more efficient computer that only does proof-of-work, but does it for cheaper - than the system breaks down. Spammers pay less than users.
Yes, there are "ASIC-resistant" proof-of-work systems in the cryptocurrency space. People specialize on them anyway - there's ASIC mining rigs for Monero, for example. Yes, you can fix that with a hard fork, but hard forks take time in decentralized systems, and designing new hash functions also takes time. ASICs aren't even the only way people specialize their mining rigs, just the most blatant, obvious, and most importantly, capital intensive.
"If you can specialize [...] then the system breaks down. Spammers pay less than users."
That's not at all what happened in practice. You see, in the Bitcoin industry, those who specialize, those who design and manufacture ASICs, realized that selling them on the open market is equally profitable as mining with them. As a result, even the small miners, the common guys, have access to the same hardware as the large scale miners. That's why today anybody can get, say, an Antminer S19. So spammers do NOT "pay less than users". We all pay the same amount of money for the same compute power. In fact, the cost curve of mining somewhat advantages small miners. The guy with a single Antminer S19 in his garage may not need to have dedicated cooling because cracking open a window may be sufficient. Whereas the large-scale miners definitely have to incur significant cooling costs. However they can cancel out these scale issues by, notably, choosing to set up their mining farm where electricity is cheap.
If you're even considering buying dedicated mining hardware, you're already way more specialized than the average user of Bitcoin. Diseconomies of scale at the high end don't stop Bitcoin mining from being an extremely unequal gated community relative to the average user with a smartphone in their pocket.
In fact, this is the main reason why the Bitcoin core development team has largely rejected proposals to, say, determine acceptable maximum block size[0] through miner consensus. How much data a miner can process is likely to be far higher than that of casual users, who aren't going to be mining and thus have no franchise.
As for the scale issues you mentioned, wouldn't dedicated cooling be more efficient per hash? That's the metric that matters for Proof of Work.
[0] Either the base block size or SegWit weight units, both of which are locked at 1kb/4kwu forever.
Proof of work is a form of money[0], with extraordinarily unequal distribution[1] in people willing to front the cost of spinning custom single-purpose mining silicon. A social media site that uses proof of work is equivalent to a social media site that is explicitly pay-to-play, where ordinary users will be censored for being too hashcash-poor to participate.
[0] That's why Bitcoin uses it
[1] That's the opposite of why Bitcoin uses it