Potential or lack thereof, isn't all that important. While most trainees would end up ceasing progress at the lower echelons, with a larger base there will always be a few lucky ones who manage to stand out.
Now, they might not have access to cultivating resources to aid their training, but that doesn't mean they can't get their hands on them after distinguishing themselves in battle in the future.
It's unrealistic to expect everyone to break free from their social class, but helping a select few outstanding individuals to overcome such barriers and create a gap in the closed Noble system is something Hudson could still accomplish.
After all, there is no law explicitly stating that Serfs can't become Nobles.
As a motivation for the soldiers to risk their lives, after each major war, the Alpha Kingdom has always promoted a few grassroots lucky ones as examples for the ordinary soldiers.