It's more like a trap 
Yes Fire Elemental is a trap: i.e. a card that appears to be strong but is in fact weak.
Here's why:
First, it is Ethereal, which means it has low health relative to its cost. And at this point Ethereal is scissors, and there are a lot of rocks in the meta: Lightning attacks, Wizard's inherent Zap, Mage Staff and others. Water attacks also do full damage and are relatively common due to the usefulness of attacking Battle Forges, pushing opponents through pain walls, etc. In short, the Fire Elemental is very inefficient against Wizards, so why include an high point cost card which will be dead when facing an already challenging matchup.
Even if you get a favorable matchup, and your opponent is not packing anything that does full damage, the Fire Elemental is still not particularly effective.
Here's why:
At 4 spellbook points (IIRC), only Warlocks and Fire Wizards will be playing the FE, and will also have other fire attacks. If your opponent is able to keep good counters to fire in play (Dragonscale Hauberk, Elemental Cloak), spending 20 mana to add more fire attacks does not necessarily improve your board position. Conversely, if a Warlock or Fire Wizard's fire attacks are working at full strength, then they are less likely to need the FE. Likely better off to diversify and bring something to counter other threats, like a demon with flying, piercing or counterattack.
At a bare minimum, the Fire Elemental would need to be revised to be less vulnerable to Lightning in order to be competitive.
