The only way to destroy this card is through other effects, or by having an equal number of Monsters on both sides of the field at any one End Phase
What affects the value of Eager Construct
Charizard, of the Pokemon sets Obsidian Flames, Shining Fates, Champion's Path, Crown Zenith, Brilliant Stars, Celebrations, Darkness Ablaze, SWSH Promos, Cosmic Eclipse, SM Promos, Unbroken Bonds, Detective Pikachu Promos, Hidden Fates, Burning Shadows, XY Generations, XY Flashfire, XY Evolutions, XY Promos, Generations, Charizard EX Red and Blue Collection, Vivid Voltage, Team Up, Legendary Treasures, Plasma Storm, Boundaries Crossed, Platinum: Arceus, Secret Wonders, Power Keepers, Crystal Guardians, Dragon, Skyridge, Gym Challenge, Neo Destiny, Team Rocket, Expedition Base Set, Stormfront, Legendary Collection, Base Set 2, and Base Set

Akroma's Vengeance Austere Command Avenge Blood Money Blood on the Snow Bontu's Last Reckoning Breaking Point Catastrophe Ceaseless Conflict Citywide Bust Cleanse Cleansing Nova Cloud's Limit Break Crux of Fate Damnation Damning Verdict Day of Judgment Deadly Cover-Up Deadly Tempest Deadly Vanity Death Begets Life Decree of Annihilation Decree of Pain Depopulate Devastation Do or Die Don't Move Doomskar Dusk // Dawn End Hostilities Endemic Plague Expel the Interlopers Extinction Extinguish All Hope Fated Clash Fated Retribution Fell the Mighty Fight to the Death Final Act Final Showdown Force of Despair Forced March Fumigate Game Over Gaze of the Gorgon Glyph of Doom Glyph of Reincarnation Guan Yu's 1,000-Li March Harsh Mercy Hellfire Hour of Reckoning In Garruk's Wake Jokulhaups Kaya's Wrath Kindred Dominance Kirtar's Wrath Life's Finale Localized Destruction Mandate of Abaddon March of Souls Martial Coup Mass Calcify Mogg Infestation Nature's Ruin Necromantic Selection No Witnesses Obliterate Organic Extinction Overwhelming Forces Path of Peril Perish

Overall, I would not think much more about it until we have a list