The uncertainty the rules talk about is in regard to the outcome of a declared action. Dice are used when the DM decides success/failure is uncertain.
Initiative is not used to resolve the success or failure of action declarations.
Thus, when a player declares an action intended to catch opponents off-guard, that must be resolved. And, yes, the DM can just grant auto-success. The correct way, by RAW, to then play it out (whether ruled automatic success or determined by ability checks) is to roll initiative but grant a surprise round.
So the real DMing question is when to reward players for good play with automatic success, and thus incentivize that kind of play. I don’t think being the first to say “I attack!” rises to that level.