TL;DR: Think of the key as a late-mission MP support Event, not an Asset. It competes with no slots, and you don't have to play it until/unless it's needed. If 3R and 1 action to trivialize an entire 3+ Shroud 8+ Clue location for EVERYBODY in your party seems worth it, then it doesn't matter when you draw your one copy- you'll always be happy to see it.
+++
I recently completed a 3P Carcosa as Tony Morgan; the key here was a late upgrade in the "eh why not" vein after getting all his other needed upgrades. It ended up being a relief to see on each remaining mission.
Left me wondering why it never really got much in the way of reviews, but I think I can see why- it looks deceptively cumbersome. 3R to play, 2 actions to place & recover, only 1 per deck, Lockpicks exist, etc. But here's the thing: in 3-4 player MP, all of these become unimportant... a single use of the key will pay for itself.
- Fast. No need to play it til you need it, and ultimately costs only 1 action to place it at a destination.
- NO SLOT. Did you notice that? Some assume the key is an Accessory or Hand item at a glance, and thus in competition.
- Item. You can tutor it with Backpack, which many Rogues enjoy running.
- You likely want it late. High-shroud spots often reveal near end of mission. This reduces the 1-per-deck risk.
- Scales hugely in MP.
That last one's the biggy. It's rare that a campaign doesn't have at least one location with 3+ shroud and 2+/Investigator clues. In SP you can clear that with an event or skills. In 4P though, the Skeleton Key becomes an 8-charge Flashlight that your whole party can use in addition to any other investigation skills they have.
If you can get the key to work on 1 hard room in a mission in 3-4 player MP, it's a terrific and reliable value. The uninstall/reinstall effect is neat, but distracts from the fact that it should pay for itself with a single use.
(FUN FACT: Preston & Dexter & Sefina aside, everyone who can take the Key has 3+ base INT, and is thus themselves now investigating at a minimum of +2 after using it.)
(edited to add Sefina to sub-3 INT investigators, thanks to all who noted this in comments!)