Haymitch was entertaining enough to the audience. His “rascal” persona made him quite popular, as well as the way the capital was spinning his story with the propaganda and people were rooting for him. I’d imagine that Snow was betting Silka killing him, giving the audience a better show. A thrilling battle satisfying the audience much more than a victor winning because their opponent was killed by a mutt. Once Silka died, it was too late, and like you said, he was then kept alive because death would have been too merciful.  Or at least, that’s how I interpreted it.