The problem with proof-of-work is that attackers can invest in powerful hardware - as your spec notes - and have an advantage over other nodes. When paying in bitcoin, as a spam prevention mechanism, no one has an advantage over others. Everyone pays the current market price for bitcoins, and even the miners - who generate bitcoins, and so don't pay the market price - can sell their coins at the market price, so it still comes down to "do I want to use these bitcoins to spam this network, or do I want to sell the coins for $575 per piece?".
Thanks for the comment. Let me know if you have any other concerns.
My suggestion was related to ratings, not viewing listings. I think that if the network reaches a sufficient size (thousands of nodes), retrieving listings won't be a problem. Hosts can simply throttle connections, and refuse to send out more than a certain number of listing to a single host in a certain time frame.
I don't see proof-of-burn as bad for the Bitcoin network. Proof-of-burn transactions are instantly pruneable, so they don't really put a burden on nodes (other than the 200 bytes they take up in storage space).
PoB tx usually do require a change output along with it's burn output, and even if we weren't concerned with that, 200 bytes is 1/5000th of a block meaning only 5000 objects can be broadcasted per 10 minute period (assuming everything in the bitcoin block is a PoB tx). In other words, it doesn't scale.