#Uncertainty

You write that the king probably won't catch deserters. That may be true. But how much should they bet on it? If the kingdom is medieval/feudal:

• Feudal levies are raised when the king calls his dukes, the dukes call their barons, the barons call their knights, and the knights round up some hapless peasants.
• The peasants do not own their farms. They have a (possibly hereditary) right to live there as part of their feudal rights and duties. Deserting now could give their landlord an excuse to evict them, a year from now or a decade from now, whenever he finds the time to try the miscreant.
• The peasants might be unable to conceive a society without knights in charge. They will gripe about bad overlords, and fondly remember good ones, but the system stays.

How do the conscripts figure to go home? Through a war-ravaged country? Without supplies? Could they read a map, if they had one to start with?

Uncertainty

You write that the king probably won't catch deserters. That may be true. But how much should they bet on it? If the kingdom is medieval/feudal:

• Feudal levies are raised when the king calls his dukes, the dukes call their barons, the barons call their knights, and the knights round up some hapless peasants.
• The peasants do not own their farms. They have a (possibly hereditary) right to live there as part of their feudal rights and duties. Deserting now could give their landlord an excuse to evict them, a year from now or a decade from now, whenever he finds the time to try the miscreant.
• The peasants might be unable to conceive a society without knights in charge. They will gripe about bad overlords, and fondly remember good ones, but the system stays.

How do the conscripts figure to go home? Through a war-ravaged country? Without supplies? Could they read a map, if they had one to start with?