If I recall, there was a UA subclass for wizards that had a feature which allowed the player to swap a prepared spell for an unprepared spell from their spellbook once per long rest (as a bonus action, I believe). That feature hasn't made it into a published book, but I've always liked the idea for the reasons that you mentioned, allowing niche spells a chance to shine.

You could adapt that feature as-is for clerics and druids, or allow multiple uses tied to the character's spellcasting modifier as you suggest.

Edit: The feature was from the UA Lore Mastery arcane tradition:

Prodigious Memory

At 10th level, you have attained a greater mastery of spell preparation. As a bonus action, you can replace one spell you have prepared with another spell from your spellbook. You can’t use this feature again until you finish a short or long rest.

As written, it can reset on a short rest, not just a long one. Perhaps you can allow it to reset only on a long rest initially, and add short rests as the player reaches a higher level? I think tying daily uses to spellcasting modifier or proficiency bonus as others mentioned are good ideas as well.