Well. You could have a repeating command block execute this command

/clear @a minecraft:carrot_on_a_stick

Once a carrot on a stick is obtained it will instantly be cleared from the player's inventory.

I think that you could have a repeating command block execute this command:

/clear @a minecraft:carrot_on_a_stick

Once a carrot on a stick is obtained it will instantly be cleared from the player's inventory.