I just popped in to say how absolutely disgusting this is with Excalibur. No more runs this turn...oh and also if you want to keep THIS run you can say goodbye to your hand. Then it turns out they're running a Shock! and they die hilariously. Or just put a Kakugo behind it for a hard kick-out. Not to mention it's essentially a second copy of the damn thing on a different server...
Unfortunately the really fun places to do this tend to be Jinteki (White Tree, AgInfusion) which is a pretty huge influence hit. AgInfusion especially could be really fun since you can just send them at the Loki server over and over and over and vary which ICE you use with it based on what their current setup is. The White Tree approach is a little more boring...just force them to run the specific central of your choice if they want to see any of your remotes. I guess you could do something like Wormhole or Susanoo-no-Mikoto to try and force them into an Excalibur subroutine, but influence starts tightening up pretty quick.
...also wait, that top ruling means you can use Loki as a repeating trap since the trash effect traps generally come with doesn't happen. There are a few hoops to jump (rez the trap without trashing it, prevent the Runner from running the trap in order to trash it) so this probably all falls into the Grade A Jank bin. Let's have a quick look at all the traps, shall we?
Data Mine: One net damage. Meh.
Howler: This seems promising...you can spew bioroids everywhere and- oh, wait, the install ability self-references so it won't work. Sad.
It's a Trap!: "Trash 1 installed card" tax for each run of the server. Might be alright, but for such an amount of setup this feels lackluster.
Kitsune: You can do a stupid Haarpsichord trick where your remote is literally just Loki and you have this stashed somewhere else, then when they try to run it you feed them a low scoring Agenda to protect the higher scoring one currently in the remove. A lot of moving parts, though. As a bonus, if they try to run at Kitsune to get rid of it you can just not choose a card in HQ and Kitsune won't trash, so you can always just do more basic stuff like throwing them at HQ traps.
Lab Dog: Trash a hardware every run. Meh. Good chance of whiffing against a number of decks, and even against decks with some hardware the Dog itself would probably do fine.
Special Offer: 5 credits per run? It's not terrible, but it's probably not worth the investment either.
Universal Connectivity Fee: Now we're talking. It's probably STILL not worth the setup and the requirement to keep your Fee from being trashed, but at least the payoff looks cool: Slap Loki behind Data Raven and the cost to get past Loki is suddenly "all your credits and your entire hand". Ouch. You'd have to dedicate your whole deck to setting this up in a way that's useful, though, and since it falls over to AI that's pretty meh.
Whirlpool: If you're triggering this more than once in a game, you're doing it wrong.
Also, am I the only one that noticed that Loki's natural subroutine stops Faust dead in his tracks? That seems kind of neat flavour-wise.