If the dungeons are so risky for minors that it's genuinely affecting the population of young people in other countries, then at that point minors just shouldn't be allowed in the dungeons at all.
Alternatively they should only be allowed with some sort of guardian (parent, school teacher, adventurer guild member, etc.) who can then lay claim the drops on their behalf. Sure this could lead to other problems like the guardian taking the profits for themselves and working the kids like unpaid labor, but that can be handled separately and should still result in less dead kids.
Letting kids roam free in the dungeon but depriving them of any income just feels like the worst of all available options.