I still think sailors looting enemies of weapons/items is fully realistic--in early modern history, looting of defeated enemies on the battlefield was often part of the expected pay from being a soldier. So, sure, the captain could do an inspection of the crew and discover they took swords from the enemy, but if they are allowed to take part in that sort of looting (as an incentive to actually risk their life and be part of the smaller boarding party, they do need some incentive beyond their couple of gold a month, no?), then the inspection discovering their loot would just justify a pat on the back for them having killed an enemy.
I think proposing absolute bars on lootings for common soldiers enforced by formal inspections sounds a bit like imposing our current military discipline on a time when it wouldn't have necessarily been the same. I did some preliminary looking into the issue, and looting on the battlefield was common in these time periods, though it looks like some of the more professional armies may have begun to take steps to reduce it in the later periods.
For privateers with signed articles, it does seem they commonly forbade personal looting, at least from the example articles I could find--makes sense, they were dividing it all and wanted to get it all in the common pot. For privateers without any signed articles and instead on salary, I would say personal looting of items and swords makes sense, as how else could you possibly convince people to risk their lives in the vanguard of a boarding action for 20 gold a month?
On the more general point of sword prices, I agree they are generally inflated. I think reducing all sword prices by 50% is a good starting point, and then maybe some could be reduced further. I have actually been playing with a 50% reduction across the board in melee weapons recently, and it makes the prices much more sensible when compared to ships and stuff. I left gun and item prices alone, since they seem reasonable.
Here is the table I have been using with all melee weapon prices reduced to 50% of original value (so with the division work already done

) (unique swords and the jeweled dagger kept at full price):
EDIT: removed the lines and uploaded an inititem.c file with the changes, but use winmerge if using, I may have changed others parts outside of this table.
EDIT2: This included in the file I posted in the reduce effects of skill thread, plus the other changes. So best to use that one instead:
Fix in Progress - Reduce Effect From Skill Items | Page 2 | PiratesAhoy!