a blockchain of their own, secured by stolen resources, would be a whole new ballgame.
Definitely possible (they could use the Bitmessage protocol, for instance) - but not worth the bother. Reliable P2P C&C channels already exist and are widely used.
What we are facing with that, is the possibility of self modifying, evolving trojans or virii using a blockchain as DNA and telepathic shared memory...
With all due respect, this makes no sense. Lay off the SciFi, why don't you.
we get beyond the first digital amoeba and then we've got complex digital life, looking for a way to survive.
Somebody did that recently. They made a full simulation of a nematode (a small worm, 1.2mm long), down to every cell and every neuron connection (some 600+ of such connections). Then they let it "roam" in a simulated environment and it behaved exactly like the real thing.
The "Whack a mole" analogy will seem a whole lot less amusing when every mole knows exactly how you whacked the last one and can adapt and evade.
Simply unnecessary. There is no need for the botnet to have such a memory and intelligence; it unnecessarily complicate things without added survival. All that is needed is for the bot herder to learn about the attacks and relay his commands reliably to the botnet - and we have that already; using a blockchain adds no benefits.