The burn time of carpets needs to be adjusted. It's 67 for normal furnace. Rounding down to 33 is the problem.

Code analysis

Code analysis based on MCP-Reborn 1.17.1 by Avoma can be found in this comment.

In net.minecraft.world.level.block.entity.BlastFurnaceBlockEntity.java and net.minecraft.world.level.block.entity.SmokerBlockEntity.java, the duration each fuel item lasts is calculated with the following method:

protected int getBurnDuration(ItemStack $$0) {
   return super.getBurnDuration($$0) / 2;
}

According to net.minecraft.world.level.block.entity.AbstractFurnaceBlockEntity.java, carpets have a burn time of 67. When the integer 67 is divided by the integer 2 in the method described above, the output value is 33. Therefore, three carpets have a burn time of 99, which is short of the time of 100 required to smelt the item.