From the position of thinking that the Fighter is fine, but that the criticism also has some merit (if delivered with way too much hysteria and hyperbole and anguish) here is my good faith effort at a house rule:
Hero Points
At first level, pick one attribute. When you fail an ability check with that attribute, you may re-roll the d20, and you must use the new result. You may do this as many time as your proficiency bonus, and you regain all uses after a long rest.
Each time your proficiency bonus increases, you may pick an additional attribute to use. You may also swap out an existing attribute for a new one.