Casters have the greatest flexibility in exploiting the system. They have hundreds of potential abilities to choose from (spells) which can target any ability score. A player who keeps this in mind can work the system in their favor and is likely to be quite powerful.
There are few non-casters with similar flexibility, though the battle master comes to mind as a subclass that might be able to effectively exploit the system. Other subclasses won't even notice the change, like the champion fighter who neither benefits nor suffers as a result of this change, since they have no save abilities. Then there are classes like monk who have a core ability that depends upon a saving throw (stunning strike) and they are likely to be very swingy under such a system. Against low Con monsters they won't be able to miss a stun. Against high Con monsters they won't be able to land a stun.
Converting saves to NADs is the more balanced way to go, IMO. Sure, the lines on it aren't anywhere as elegant, but there's a reliable engine under the hood, and IME that's what matters more when you're actually playing.