The rules of 5e emphasize that when players declare actions, it's best to specify both a goal and an approach. Nothing in the 5e rules suggest that that pattern should apply to 5e's other resolution mechanics, like saving throws.
So I agree that saving throws don't adhere to "goal and approach", but under the broadest definition of that term in the 5e context, there is no reason to expect them to.
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I can't agree with your assertion that 5e's rules call for ability checks to only be made as a result of player action declarations. Yes,
when players are declaring actions, the rules say they should state their goal and approach and then the DM should then determine whether to call for a roll. But I don't see any support in the rules for the claim that all ability checks must follow this pattern.
Numerous elements throughout the rules suggest otherwise. Examples:
- Ability checks can be used to resolve monster actions in addition to PC actions (PHB: "An ability check tests a character’s or monster’s innate talent and training.")
- The rules call for certain active ability checks to be used defensively (e.g. when PCs/NPCs/monsters without special grab abilities initiate grapples, the target makes a contested active ability check).
- The rules specify that passive Wis (Perception) checks are used defensively when resolving opponents' Dex (Stealth) checks.
- Ability checks can substitute for saving throws to see if a character avoids a new hazard (e.g. "stay upright on a rocking ship’s deck" Dex (Acrobatics) example in the PHB).
All of these examples are cases where the rules explicitly call for or permit ability checks in situations other than the resolution of player action declarations.