Because anyone who tried that got burned with child porn and the threat of real prison time.
p2p tech is fundamentally incompatible with American morals. You will never see a p2p based firm be successful in the US any more than you could have had the industrial revolution in Ancien Regime France.
Each user storing what they post doesn't really scale. If I have a 100kb image in a post that gets popular, then the following technical things are needed:
1) It needs to work reasonably fast when the suddenly popular post is seen by, say, 10000 people in a short time. My home uplink won't handle that.
2) It needs to work when my computer is turned off or disconnected from the internet.
3) (optional, but still important) People on the other side of the world should be able to get popular data from a cached copy that's physically closer, both for latency and bandwidth reasons.
"Store what you post" isn't sufficient, all that I post needs to be stored also by someone else (e.g. a CDN) - but that immediately rises all kinds of issues about liability. If only I am storing what I post, then the system can afford to not care if that image turns out to be child porn, but if someone else is storing what I post, then that's a problem for everyone.