For reference, as of The Circle Undone, here is a list of negative effects that Eldritch Inspiration can be used to mitigate:

Alchemical Transmutation - Take 1 damage.
Astral Travel - Discard an item or ally asset from play, take 1 damage if you cannot.
Blinding Light - Lose 1 action.
Blinding Light (2) - Lose 1 action and take 1 horror.
Mists of R'lyeh & Mists of R'lyeh (2) - Choose and discard a card.
Recharge (2) - Discard the chosen asset. (Note: You still don't get the 3 charges in this case.)
Rite of Seeking & Rite of Seeking (2) & Rite of Seeking (4) - Lose all remaining actions and end your turn.
Seal of the Seventh Sign (5) - Remove 1 charge from Seal of the Seventh Sign.
Shrivelling & Shrivelling (3) - Take 1 horror.
Shrivelling (5) - Take 2 horror.
Storm of Spirits - Deal 1 damage to each investigator at your location.
The Chthonian Stone - Return The Cthonian Stone to your hand.

Here is a list of positive effects that can be doubled using Eldritch Inspiration:

Eldritch Inspiration - Can actually be used on a second copy of itself, but it won't quadruple the effect it will just triple it.
Hypnotic Gaze - Deal an attacking enemy's damage to itself.
Jewel of Aureolus (2) - Draw a card or gain 2 resources.
Recall the Future (2) - +2 skill value for this test (named , , , or token only).
Ritual Candles - +1 skill value for this test.
Song of the Dead (2) - +2 damage ( only).

Note that and on cards will count as triggers for this card, as per the Rules Reference. Father Mateo doesn't actually get an additional benefit from repeating his conversion of to , and Jim Culver's to 0 conversion is static and not a trigger.

Don't sleep on this card!

The real power here is in gaining back a bunch of resources from a spent item while also gaining tempo by dealing 2 damage for 0 resources. Cards that grant click compression tend to be among the best cards in the game. The "if you succeed" clause is also generally fine coming from the faction with both Lucky! and Live and Learn.

So what deck can use an Act of Desperation? Honestly, anything with Backpack, it has almost perfect synergy with that card and deckbuilding style. Mark Harrigan puts this under his Stick to the Plan to recoup the investment on his Lightning Gun or M1918 BAR. Survivors tend to be swimming in cheap items and card draw so it can act as a backup to Fire Axe (at least until they all upgrade to Ornate Bow or Timeworn Brand).

Then on top of all of this, the card has symbols like so much gravy.

I like most of the new tarot cards (Ace of Rods being the only exception). Advantages:

• Provides +1 , which is necessary to deal with enemies that prevent clue gatherers from winning the game
• Free to play if in opening hand (mulligan increases your chance of drawing it)
• Does not conflict with existing assets with the new tarot slot
• Is not an item, so it's immune to many treacheries that target these

Disadvantages

• Second copy is a dead card, as players have only one tarot slot and it has no icons to commit
• Conflicts with other tarot cards, if the investigator has access to more than one faction at level 1+
• Ability to play this for free may motivate a player to mulligan important cards, like weapon assets
• Guardian assets are quite expensive, so 3 ressources can be too much

I like most of the new tarot cards (Ace of Rods being the only exception). Advantages:

• Provides +1 , which is the most important stat to gather clues and win the game
• Seeker assets are rather cheap, so 3 ressources should be ok
• Free to play if in opening hand (mulligan increases your chance of drawing it)
• Does not conflict with existing assets with the new tarot slot
• Is not an item, so it's immune to many treacheries that target these

Disadvantages

• Second copy is a dead card, as players have only one tarot slot and it has no icons to commit
• Conflicts with other tarot cards, if the investigator has access to more than one faction at level 1+
• Ability to play this for free may motivate a player to mulligan important cards, like weapon assets

I like most of the new tarot cards (Ace of Rods being the only exception). Advantages:

• Provides +1 , which by itself helps evading enemies and protects against some treacheries. It's real value lies in cards like Lockpicks.
• Free to play if in opening hand (mulligan increases your chance of drawing it)
• Does not conflict with existing assets with the new tarot slot
• Is not an item, so it's immune to many treacheries that target these

Disadvantages

• Second copy is a dead card, as players have only one tarot slot and it has no icons to commit
• Conflicts with other tarot cards, if the investigator has access to more than one faction at level 1+
• Ability to play this for free may motivate a player to mulligan important cards, like weapon assets
• Evading enemies usually does not win the game, so boosts are not as good as or .