What impact would it have on D&D and similar games if ability scores were not "always on"?
DEX bonus to Ac only being counted when a the character was focusing on defense, STR bonus to damage only coming into play when using a two handed weapon... and so on.
Would player choice in active play be more meaningful if otherwise common modifiers were tied to direct play choices and were not always on? Situational modifiers can get picky and forgotten when cluttered among a host of other modifiers but if ability modifiers are only applied on a situational basis they become the scores to modify a situation and there are only a few of those on each character sheet.
Radical crazy, maybe. But without high ability scores being "always on" a player has to make choices beyond character creation and maybe not lean on high ability scores over tactics.