I'll compare this to Spectral Razor since they fill many of the same use cases

Pros:

• Testless damage. Depending on your difficulty this could be very valuable
• Potentially Costs 1 less if you're targeting low health enemies like Acolytes
• Synergy with arcane slot increasing effects such as Familiar Spirit
• Synergy with empty arcane slots, clearing the way for a beefed up Eldritch Initiation

Cons:

• Anti-synergy with standard arcane slot spells (unless you managed to spend all the charges already)
• Must be engaged. Razor comes with a free engage to deal with pesky aloof enemies
• Increasing the damage potential still requires you to pay one more resource per damage. You can easily reach Dynamite Blast cost but for situationally less payoff since you're always targeting just one enemy.
• Only target non-elite. This a deal breaker.

In my opinion the best reason to run EW over Razor is to lean into that big payoff explosion. This requires you setting up assets to maximize your slot conversion which will be a significant resource and card investment. All of that setup to be able to target basic enemies only is a let down.

For most investigators Razor will get you more mileage. The only Mystics who I can see potentially taking Ward are those who cant reach useful + scores (so just Marie Lambeau?)

I'm playing Lily right now through Innsmouth, and originally I planned to upgrade out of this card pretty early. I no longer want to do that, because this card is fantastic in a focused Lily deck with Runic Axe. Just use your friendly neighborhood amateur witch to find it! This is basically an Overpower that you just draw into, and that's perfectly good.

This isn't a tool you'd want to use on high- mystics - they have more efficient ways of getting solid hits in. However, this can shine in the hands of characters who want to occasionally help do some damage without committing a bunch of resources, and don't otherwise have the stats to back up a more normal attack.

The fact that it's a level 0 card means it can slot in a lot of characters with little effort, and it can quickly be dropped once you have a better tool for the job. I don't think this works well as a build-around, but it slots well for character who want access to a testless nudge of damage. Spectral Razor is a more flexible tool, but there are definitely characters with low-level mystic access who can make more reliable use of this.

For reference, as of writing, the list of characters who have access to Mystic 0 cards and have total Combat+Willpower of 5 or less (to compare with Spectral Razor include Carolyn Fern, Mystic Carson Sinclair, Mystic Charlie Kane, Daisy Walker, Mystic Mandy Thompson, and Rex Murphy. I don't think this would go in all of their decks, but I think the card is efficient enough to be worth considering in such a place.