That site wouldn’t have any spam, true. Though not because of the cost, but because it wouldn’t have any users to make it worth spamming. No one wants to pay per message. Everybody would be too nervous and quadruple-thinking “is this message worth a cent?” Once in a blue moon someone would post, get no reply, and be even more unlikely to post next.
And yes, yes, not literally everyone, but enough that it becomes a rounding error.