@agtra I don't really think surrender was ever really an option for Jurgen to be honest. Given his inner monologue at the beginning of the chapter, I think he always knew that all his actions would amount to was a sacrifice play to buy for time. His job was to ambush the enemy's flank, interrupt supply lines, and make them waste time regrouping before resuming their march and advancing more slowly while looking out for future ambushes. This would allow the rest of the 1st prince's faction to fortify Ingolstadt and coronate the 1st prince as King, then flee south to an allied nation where they could establish a government in exile and return in the future with tons of foreign military support. It's not like they would've been spared if they just surrendered. If they had succeeded and bought enough time for their fathers and the 1st prince to have escaped, then they would've been held responsible for the civil war as the heirs to their families and executed as traitors. If they had failed and their fathers and the 1st prince were captured, then they'd still be held responsible for the civil war and executed as traitors. It's not like the 2nd prince would suddenly become magnanimous and welcome the nobles that sided with his brother back into the fold. You can bet that at the end of the war, a lot of the noble houses are gonna be put under for either siding with the 1st prince or failing to aide the 2nd prince. The 2nd prince is going to start consolidating his power and probably begin the process of centralization as well. He needs a military loyal to him as the future leader of the land, not a bunch nobles with their own private armies that could suddenly stab him in the back once a succession war kicks in.
Back to Jurgen, he and his fellow classmates were a symbol of an older generation's romantic ideals about war and the place of the nobility in modern society. They were slowly becoming obsolete in face of society and the military marching towards modernization. He could see a preview of that during his trip to Weiβen. That last charge against 2nd prince's forces and the Weiβen reinforcements was just a matter of choosing the time and place of his end. That they got cut down by volley guns and modern firearms wielded by commoner professional soldiers was just a matter of poetry. He lived by romantic ideals and died in a symbolic way that he felt best conformed to them.