Yes you can certainly achieve that in less than 10 minutes, but it comes at a high cost, just as it does in PoW coins that use 30 second or 1 minute blocks, or somewhat more speculatively, even faster with tweaks such as in ETH.
Bitcoin uses 10 minute blocks to keep reorgs and centralization pressure within "acceptable" limits. Obviously 10 minutes is not the perfect number, but both increasing and decreasing have clear tradeoffs.
In the case of p2pool, for example, even the small share of hash rate represented by p2pool includes a portion that is effectively centralized pools that use p2pool as a back end. The reason is the high cost in bandwidth and latency tolerance of p2pool exerts additional centralization pressure on top of what already exists in Bitcoin, so you end up with a second tier of centralization.
Thanks for the thoughtful reply, I'm glad to be able to read your words when you really apply yourself instead of posting dismissive single sentences.
The "high cost" of p2pool as it is right now is because it applies to full, high hash power into the lower-level blockchain with fast blocks (less than minute).
When p2p-pool idea would be applied to the propagation tracing only a fraction of hash power would be applied to the fast-chain. The majority of hash power would still go to the slow, decaminute normal Bitcoin chain.
When p2pool would be used just as a proof-of-propagation the required fraction of total hash power would be rather low, probably around single percent. Therefore the cost of orphans would also be insignificant in comparison to the total hash power. I'm not going to repeat the whole analysis done in Microsoft Research's "Red Balloons" paper. Interested readers could easily find it themselves.
The general idea still stands. Why it isn't getting much interest in Bitcoin milieu is a different story, rooted in political-science not in computer-science.