The current logic for weapon distribution works as follows:
There are four rounds of distribution. In the first round, weapons that fully match the type are distributed, and for cavalry, if it’s a polearm, it must be a lance; infantry cannot have lances. The second round matches one subtype (e.g., 'one-handed sword'). The third round requires a match in the broader type (e.g., all are one-handed weapons), with the same rules for lances and cavalry as in the first round. The fourth round only needs the broader type to match. Throwing and melee weapons will never be allocated to the other's slot. Higher-tier soldiers are prioritized in distribution, with suitable weapons sorted first by tier then by price, chosen from highest to lowest. For infantry, weapon attributes like bonus against shield, ability to dismount, knock down, or brace as a spear each count as +1 tier. If there are still empty slots after four rounds, surplus arrows, shields, throwing weapons, and two-handed/polearms are allocated based on what the soldier already has.

I think allowing players to configure their own distribution settings is feasible, though it might be more complex than described, as it involves prioritizing weapons and choosing alternatives when preferred ones are not available. I might add this feature in the future.