I really don't see why this requirement exists. Having fairies spawn more often around them is fine, but not being able to get them at all should you unwittingly destroy all the logs is potentially very annoying.
Yeah I tore down most of the logs in my first 1.4 world when I noticed they took more than one hit to break and realized they probably give wood. Too late did I learn that I could have caught fairies near them.
Perhaps moving them to Living Trees would be better?
Traditionally people built fairy houses to put up gardens and patches of private woodland out of superstition, so it'd probably make sense to have it as a sawmill constructable object to return the cost of wood back in some way. A debt repaid and keeps fairies where you want them.
See also: Placement Objects, or background objects, are a general type of tile which occupy space but can be passed by the player. Blocks cannot be created on top of them until they are removed. Most types of objects are scattered across the world during world generation, though some (namely...
* Fairy Logs: 30 pure wood + 10 pearlwood + 1 of each fairy with Sawmill in Graveyard.
* Broken furniture rubble: Corresponding furniture with any anvil in Graveyard.
* Cobweb rubble: 10 webs per tile it occupies with Loom in Graveyard.
* Bones: 25 bones per tile occupies with Bone welder in Graveyard.
* Rocks: 10 stone per tile it occupies in Heavy Workbench next to anvil in Graveyard.
* Rocks with gear stuck: 30 stone + Miner's helmet, or Lead/Iron pickaxe, or Lead/Iron sword in heavy work bench next to anvil in Graveyard.
* Broken gear: Corresponding gear (wooden arrow, iron/lead sword, miner helmet, etc) + autohammer in Graveyard.
* Mossy/Grassy rocks: 1 moss/grass seeds and 10 stone per tile in Heavy Workbench next to anvil in Graveyard.
* Gem rubbles: 1 gem and 5 stone per title in Heavy Workbench next to anvil in Graveyard
* Tent decor: 25 silk, 2 iron ore in Loom in Graveyard.
* Pile of dirt with shovel: 100 dirt + shovel by hand in Graveyard.
* Wheelbarrow full of dirt: 25 dirt + 10 iron/lead bars with anvil in Graveyard.
* Post with rope: 10 any wood + rope coil with workbench in Graveyard.
* Altars: Demonite/Crimtane + Luminite Ore with Crystal Ball in Graveyard.
* Stalactites/Stalagmites/icicles: 5 of the block corresponding its appearance per tile.
Altars placed by players do break when hit with a hammer, and do not generate ores, the rest of the rubble would work just the same as the original.