Too long of a read? No worries, check the bottom for a tl;dr
I don't really like the Trade Inn (besides the minigames) because the spools system dominates it in terms of value and chance. You can not only earn more curios over time with spools but you can also choose what you want, in contrast to the Trade Inn which gives you a random item of greater rarity in exchange for 9 items of a lesser rarity. It's like gambling for a prize when instead you could use that bet money to buy the actual item you want for much cheaper and without having to try your luck.
So is there really much of a reason to use the trade inn? Not really, but maybe you could that it would be good during special events when it's boosted or something, or if you want to dispose of a bunch of extra t-shirts quickly. Even then, it's not a guarantee.
I suggest that the Trade Inn is changed to include heirloom quality skins (or others that don't drop anymore) at a very low chance. The reason is that they are no longer available as drops which means the eventual decline in circulation. I think this can be a fair tradeoff for the higher overall net loss. Heirloom skins are tradeable, unlike their weaveable counterparts, and I thought it'd be fitting that by exchanging tradeable items, you should earn a tradeable item. This encourages hardcore collectors to be able to have a better chance of getting heirlooms (such as console players not having access to Steam community markets). Even if you don't like or care about heirlooms, the greater spool value pays off in exchange.
Another option could be to include Klei Points as a random prize instead, also at a low chance. If you're a late joiner to the game and don't have all the loyal skins from the Klei rewards page, it can be a way to speed up the collection progress without having to wait for updates. Somewhere around 100 points would suffice for an icon, or to save up for that nice belonging skin.
The Trade Inn could potentially include chests as well, sort of a way to earn them outside of events to either collect them for the sake of it or as a nice bonus when you get lucky. This could be the Winter's feast chest or something similar, maybe Forge or Gorge chests?
My last suggestion would be to enable some sort of method of assurance or guarantee to the Trade Inn. This could be trading in a certain set/theme of items, paying a premium with extra spools/extra curios or character-specific clothing. Think of it like in the crafting menu in Team Fortress 2. You can craft those "character tokens" that guarantee a random item specific to that character, such as a hat or weapon.
In order to apply this to the Trade Inn, it would be interesting to see implementation of something like trading in a majority of blue-colored clothing to have a higher chance of earning a blue-colored curio. Or maybe throwing in a character-specific item like "tuxedo gloves" heightens the chance of earning other curios specific to Wilson, since "tuxedo gloves" are a part of Wilson's survivor filter. Or trading in a set of warm clothing can grant Winter-themed outputs. Or even a combination of all of these factors. These are just a few to name, and the possibilities are endless.
TL;DR: The trade inn should have a chance to give heirloom skins, Klei Points, or chests. There should also be a way to improve chances for certain outputs by modifying inputs too. This encourages people to use it more often because of the greater potential value they earn out of it and the greater sense of control over the output.