There are two sort of players that might use Eridium: new characters leveling up, and end-game players (or more if I’m forgetting something).
If I’m leveling up a new character, Earl’s vending machine lets me buy on-level, anointed Epic gear. He’s priced where these aren’t cheap for a rookie character (without a modicum of farming for Eridium), but unlike the Golden Chest where it’s a dice roll for what comes out of there, one can refresh their arsenal with some strong gear from him. Also, if I’m into some of his cosmetics, that’ll be on my shopping list, but that’s a one-time buy.
If I’m at end-game, I’m likely not strapped for hard-hitting gear. I’m looking for something specific. Giving Earl story mission gear for sale is an easy one, but just kind of expands his role a little (once I have this gear, Eridium goes back to being useless currency). The slot machines are cute, but unless I’m a gambler at heart and just like playing period, they’re just sort of a novelty.
Good end-game Eridium sinks may be some sort of gear acquisition/improvement mechanism (like Earl’s vending machine, but he won’t find much business without Legendary gear therein, and I don’t think they’re going to go to a, “upgrade your gear by spending Eridium” model). TPS also had the Loot Grinder that could be spiced up with Eridium which was a pretty good sink, but I also don’t think they’ll bring this back.
The other good sink was putting some content behind it, like raids in BL2. If I was about to max out my bank in BL2, spawning Dexiduous would eat that up nicely. I mean, I was only there for the pre-Dex mob (and would usually quit after they were down and Dex came up because they were way more fun for me), but still.
If they made, for example, the equivalent of some Torgue-style Bar Room Brawl, and put it behind Eridium instead of Torgue Tokens, that would siphon off my Eridium pretty quick at end game. Therefore I would suggest themed Bar Room Brawls… sort of like Circles of Slaughter but distilled into a single, brutal, dense wave of some enemy type.