No, the prosecutor isn’t there to secure a ‘win’, he’s there to make sure the case-as-it-happened is put before the jury. That’s why Grosskreutz had to speak, even if sunk the case. It would have been completely unethical to have held him back.
In principle you're absolutely correct, but the body language of the guy who facepalmed after Grosskreutz' testimony confirmed that Rittenhouse didn't fire before he had the gun pointed at him would indicate a rather unprofessional behaviour in that sense. When the prosecutor spoke of what I heard, it came across as preachy. Like when they hailed Grosskreutz for being an upstanding medic, yet 'forgot' to mention he also brought an illegal gun to the protest and pointed it at someone.
I'm glad Grosskreutz is alive but there's no need to paint a rosy picture of him. Just like Rittenhouse he was a stupid guy with a gun. That category were the only ones with guns around there and like I mentioned before, there are no winners in this trial. The final outcome is that Rittenhouse avoids taking the literal L and that there were two deaths that didn't need to happen if not for the crazed US gun culture.
I hope lessons are learned from this and that we won't see similar tragedies in the future, but then again it's the homeland of mass shootings and reckless discharges of guns so that's a faint hope I suppose