Based on the list of Decorate Statues on the wiki, I have some statue ideas that could provide new mechanics.
Aura Statues - When activated, these will create an aura around the statue that will provide a buff to the player as long as they stay in it and will count down after they leave the aura just like Honey. For instance, Potion Statues could increase the chance of not using materials while crafting like the Alchemy Bench does or provide an increased duration of buff potions when used. The Anvil Statue could do the same as the former, giving players the chance to keep materials when crafting regular items (though it may only work with items on the anvil itself). Perhaps Shield Potions could increase the defense of the player just like the Dryad's ability. Or perhaps the Gloom statue provides a debuff to the player and / or monster causing them to get slowed while in the aura.
Aura statues could modify non-entities as well. For instance, the Boomerang and Bow statues could affect boomerangs and arrows while inside the aura, causing them to increase in velocity and damage while inside the aura but losing those properties when outside of the aura.
Ground Modifying Statues - These are similar to the Aura Statues but only modify the ground within a certain radius. When these statues are active, the affected ground glows (or maybe has a particle effect on it) and causes changes to NPCs or the environment. For instance, the Tree statue could increase the growing speed of plants and trees (though this may work better as an Aura statue for those with pot farms), the Cross and Corrupt statues damages enemies on the ground depending on their alignment, and the Gargoyle statue slows enemies significantly. The Cross / Corrupt statues could also work as ways to spread Hallow & Crimson / Corruption respectively. It could also be used to treat specific areas another Biome. For instance, perhaps activating a Cross statue at the Ocean would allow Hallowed enemies to spawn as well.
Buff Statues - When right clicked after being activated, they provide a buff just like the Magic Mirror. Fairly simple stuff. Examples could include increased mining ability from the Pickaxe Statue, increased speed from the Boot Statue, Sword / Bow / Spear statues increase the abilities of those items, and so on.
Trap Statues - These are statues that work as attacks either on a timer or when enemies are close similar to minions. For instance, a Bow statue would fire an arrows, the Sword statue would slash all around it, the Spear statue would stab left and right, and the Boomerang statue would fire a boomerang. It would be interesting if these statues could attack players, adding an interesting trap mechanic for both PvE and arenas / dungeons for players to traverse. It'd also be interesting if you could upgrade / modify the attacks as well. For instance, a normal wooden bow with wooden arrows would be fine but how about a Hellwing Bow with Wooden arrows, a Shadowflame Bow, or just a normal Bow with Venom arrows or Ichor Arrows or Cursed Arrows. It would add an interesting level of complexity though Bows would be the only one you'd have to refill. (Gun, Rocket, and Throwing Item statues would also be pretty rad)
"Pet" Statues - Some of the statues have enemies in them but they could be just cosmetic ones. A Bee Statue, for instance, could light up when activated and spawn harmless bees that fly around the statue. Same for Imp, Gloom, and Corrupt Statues.
Other Notes
- Statues could be given more effects to show that they're active. Aside from the auras, it would be interesting to see a particle effect or a moving part of the statue like a turning of the Pillar in the Pillar statue or a filling of the bottle in the Potion statue.
That's all I can think of, hope it helps!