I'm trying to see a way for burning the coins to be useful in some way, but I'm not yet seeing it in your scenario. If it were the case that there had been a theft, and the thief wanted to be able to spend a fraction of what they stole (instead of get it all blacklisted), wouldn't the deal involve sending the remaining fraction back to the original owners? If you steal something from me, I'm interested in getting (at least some fraction of) that thing back, not in you provably destroying some fraction of it.
It is pretty much a prisoners dilemma. If the coins are blacklisted, then both the Hacker and the victim are in a lose situation and it is a stalemate.
Now let's imagine the victim tells the hacker they are not willing to negotiate and hope that law enforcement will catch the hackers like they did in the Bitfinex case. The hacker could destroy some coins every X days to make it clear to the victim that this is not a good idea.
This is just a wild scenario. But had I been the Bitfinex hacker I would have done crazy things such as sending blacklisted coins in small amounts to many random addresses, those of exchanges, developers, non-profits, Satoshi Nakamoto etc.. Just to create chaos as it would have caused those people a lot of trouble and would have forced some kind of resolution.
FWIW, bitfinex was willing to buy the coins back on what they claimed was a no-fault basis and even put a significant amount of coins into third party escrow for that purpose.
Back in the early days of Bitcoin... Zhou-tong, after robbing his own business (Bitcoinica) blind, did something kind of like what you were suggesting -- raining down coins on random people and creating general chaos. I think it was more mania and panic rather than a well considered strategy.
I think in general you don't see stuff like that through a mix of (1) it's less easy than you think, and (2) thoughtful people don't become serious thieves in the first place, it's not worth it.
For this analogy to fit, the bank robbers would have to destroy (some of) the notes/coins/gold bars (that is, the stuff both parties care about), not execute people (whom the robbers don't care about but the other side do). Which would convince the other side not that the robbers are serious, but that they're idiots.
Well, if you don't have hostages, demonstrating that you're capable of destroying the entire bank vault if they don't let you walk out with half makes sense
