I think you are applying WAY too much rationality to this. Comic book villains (villains of many stripes for that matter across media) don't always act in firmly logical manners. To say that he wouldn't want to kill Steve and his buddies because, "Oh, hey man... I know I have to wear a mask for the rest of my life, my cushy job as a Hydra employee was just taken away, I spent a couple of years doing skin grafts and learning to walk again, all because you and your pals had to do their hero thing... But no hard feelings, cuz, really, it's not personal and I can separate my professional and private life."
Sorry... It would be RIDICULOUS if Rumlow DIDN'T want a piece of Cap and crew out of a sense of revenge. People are emotional. We aren't logic machines.