This is wrong.
The taunt ability as I outlined in my initial post is explicitly not supernatural.
Non-magical and non-supernatural features can obviously affect the minds of people
1: The deception skill is a trivial example that influences the mind of a target. You lie to them. They may or may not fall for it.
2: The frightful presence of a dragon is another one, one that compels movement.
3: Menacing Attack: "When you hit a creature with a weapon attack, you can expend one superiority die to attempt to frighten the target. You add the superiority die to the attack's damage roll, and the target must make a Wisdom saving throw. On a failed save, it is frightened of you until the end of your next turn." Ie the mind of the target has been affected.
4: The Battle Master's ability that grants an ally the ability to take an extra reaction is not about compelled movement, but demonstrates that you can have abilities that are non-magical and which grant movement to other characters.
So I have proven that the system as it is already allows the non-magical characters to influence the minds of opponents. Therefore the taunt is realistic.