I thought about something like that too, but as Svanto's already mentioned, it would be kind of abused if not implemented right.
My suggestion for this is make it so you can only sell them at the hubs (Moorcroft, Emeberlight, and the Core). That way if you decided to save your vials from the previous floors, you can sell them off instead of just having them poof into oblivion. It would bring a little more use to the Arcade since you could technically make more money if you don't use the vials.
You could even expand on it more by making it so that the vials from the earlier depths are worth even more further down. So if you save a vial from the first two stratum and take them all the way down to Emberlight or even the Core, they'll be worth quite a pretty penny.

Or if the prospect of introducing more Crowns is too taboo, you could go with Vlad's idea or make it so that there's a NPC who would upgrade your vials to the next level at the hubs.

The more money you can get the less its worth duh
selling vials should not be an option, depositing them might make it to easy - so no

Uh-huh.

No -1

We've pretty much established that the OP's original idea of the machine on every level would be kind of broken. The idea of being able to sell them to Basil or another NPC at Moorcroft, Emberlight and the Core would be much better.

@Zeddy
Most players that I've played with haul around every single vial anyways, even without an added reason to hold onto them. All throughout the Black Kat event, every time I'd reach the end of the mission, the party I was with would throw every vial they had in celebration.
I agree that we don't need less reason to hoard the vials. (I personally never use them just so I don't keep getting them on the prize wheels.) But we need more incentive to use them as well. Right now they're good if you want to inflict a certain status, but it relies on the random number gods to give you the ones that you really want. Honestly the only vials I ever use are the Poison and Curse vials for healing enemies. The other ones are a bit lackluster in my opinion, especially since nearly every weapon in the game has some status associated with it.
So why use vials in the first place?
If they packed a bit more punch to them, it would make this idea much more viable, since you're denying yourself from using an actual useful item just for a little more profit. So buff vials first, then we can add this.

The only thing that matters is making money. Gameplay is not important. In fact, they should remove all content from the game except costumes, accessories, and a magic button that you smash your face on that automatically trades both kinds of energy for crowns. Your screen will only show your costume setup that you can mix and match all you want until your eyeballs implode. No one will need actual weapons, shields, or armor anymore because all of that also becomes crowns to buy your next prettiest pink dress with all the frills that can possibly be on one item of clothing at a time without destroying the universe. Once you collect all the pink panties and transparent bras available in this game your knight and all their items are automatically deleted, your computer blocked from ever accessing the game again, and at least four hitmen are already on their way to complete your Spiral Knights experience.

On top of spaghetti.
All covered in bees.
Stop dumbing this game down.
I will eat your knees.

Have you tried tossing a stun vial before? It's like a little BAB you can throw. Maybe other vials could have similar additional effects as a buff?

That or just boost their radius.

http://lmgtfy.com/?q=site%3Aforums.spiralknights.com+sell+vials

I'm just showing that this idea has been discussed to death. Being able to sell vials and pills would just promote not using them even more. Not to mention, since when you sell items, only you get the crowns, (instead of being shared around the party) everytime a vial dropped, it would be a mad, bloody, and gory dash to pick it up.