Hi aleksej, I meant not to change bitcoin mining in any way, but for nodes to, instead of throwing the best PoW away (when failing to mine that round's block), to send the failed block to one connected peer (this will work better for small blocks, with just a handful of transactions in the block's body).

With that particular coinbase and considering the exchanged information, the connected peer can verify that the failed block's miner was doing it dedicated to that peer. Since the miner must choose who is getting his dedication on each round, this seems suitable for preventing spam. And it will increase the network's hashrate. I believe a higher hashrate is certainly good for the network.

This doesn't change the reward mechanism, but would be a soft-fork instead, where nodes will require higher dedication (when under message or bandwidth stress) in order to communicate with other peers at all.

This is the idea that a failed block is still lightly useful (not for Bitcoin purposes, but for networking): a spammer will increase bitcoin's hashrate, increasing it's security. On the other hand, as you said, "miners are allowed to spam"; and "spammers may get rewarded" (by actually mining bitcoin), which kind of sucks, but well..

edit:
> But I see that you are proposing a single mining system where you get rewards in Bitcoin for your anti-spam efforts.

Well, mining has always been spam prevention: preventing blockchain block insertion spam. And also functions to increase older data immutability certainty.
PoW has always been used for more than one purpose..

edit: if some block limit of ~100kB is considered (for dedicatory purposes), then it's likely that "actual miners" won't bother letting go of 900kB for a "you may spam the network free pass card". That is, anti-spam + mining would intersect under 100kB, but >100kB would still be just plain mining. Since "serious business" miners will have more than enough "dedication credit", they won't miss it.
This will at least lower bitcoin rewards for lucky spammers.