What good are all the golden swords looted from zombie pigmen?

No, the swords that Pigmen drop are useless, unless you want some things to enchant lvl 1 when so you can change the enchantments in the enchantment table. If you are playing modded you may be able to turn the swords into ingots but if you are playing vanilla the first option is the only option I am aware of.

They provide a good source of, well, golden swords.

You can craft 2 partially broken golden swords together to get a repaired one. Other then that, as Dark Afterburn said, there's no use of golden swords in unmodded Minecraft.

If you're doing a pigmen farm (to gather XP and some other of their drops), you can use these to kill them without damaging your personal sword. But they don't have a better use.

You can:

1. Enchant them with lvl-30 enchants and use them against the zombie pigmen!
2. Drop them all one at a time into a pit of lava!
3. Put them in a chest!
4. Combine them all together into one uber-sword!
5. Throw them at zombies!
6. Make a giant wall of item frames of golden swords, and rotate them to make a maze!
7. Use hoppers, dispensers and item lifters to make a continuous golden sword waterfall!
8. Make a gold sword sorting system and try to collect one of every enchantment!
9. Mine diamonds with them!
10. Throw them at endermen!

The sky is the limit really, just up to your imagination and creativity. After all, isn't that what MineCraft is all about? :)

You can use Gold Swords to quickly cut down cobwebs found in underground mineshafts.

I would use them at the Enchantment Table to reset the enchantment list, to get your desired enchant. (For this purpose, use the lowest level enchantments) If you still haven't got what you desired, you can combine them at a Crafting Table to lose the enchantments put on them and then give it another shot. Repeat this until done. (Note that sometimes it may still not work)
Otherwise, I haven't found any other good use for them. You can't make gold out of them, and they are poor at slashing(attacking) and have a horrible durability.

I'm building a huge afk gold farm on the roof of the nether and collecting the gold in hoppers that put all the items through a filter. Gold nuggets go in one chest, rotten flesh in another, and gold ingots in the last one. The gold swords just go on through, and a dropper shoots them down to the bedrock to despawn cause I don't think there's any use in building some huge storage area for them at the farm. It's not worth it. They're practically worthless when I have a diamond sword with max enchants, and plenty of options to get Xp to repair it with. So if you ask me, don't even bother trying to get all of them, just trash them.

As of Minecraft 1.15.2, you can use the dropped gold swords to get additional gold ingots. Here is how:

1. Collect the gold swords
   a. If they have enchantments on them, put them into a grindstone to salvage XP from them.
2. Put the sword(s) into a furnace, and smelt them. It is preferred that you use an automated smelting system, as loading each sword into the furnace may be rather tedious.
3. Each sword smelted will output 1 gold nugget.

I hope this helps.

I find that random golden swords are useful for resetting enchantment table enchantments by getting the cheapest one and letting them refresh. You can use them as non-stackable items in an item sorter, but that is pretty pointless. Best thing in my opinion is just smelt them in an auto smelter as part of an afk farm.