There was an Unearthed Arcana release including a Wizard subclass called Lore Mastery. The development of this subclass was largely abandoned, although some of its features inspired a later UA subclass, the School of Invention.
One of the features abandoned with the Lore Master, the 4th-level Spell Secrets feature, allowed the caster to change the ability of a saving throw forced by a spell, once per short or long rest:
When you cast a spell with a spell slot and the spell requires a saving throw, you can change the saving throw from one ability score to another of your choice. Once you change a saving throw in this way, you can’t do so again until you finish a short or long rest.
I've permitted a player to use the Lore Master, including the save changing feature, in a campaign despite the abandonment of the subclass, since we both really like the concept. We've rarely seen the feature put to use, although in those few uses it has been interesting, helpful, and free of issues for us. However...
What are the ramifications (in terms of balance implications, exploits, and problematic rules interactions) of a feature that allows a caster to change the ability for which a spell forces a saving throw? Assume the feature has a limited use, such as once per short or long rest.
Despite the background I've included, I'm interested in a general answer for any spellcaster, not just a Lore Mastery Wizard using that specific feature.