Not always. Against some offenses you play zone coverages. Against the option, you really need to play a "man to man" or "assignment" style of defense. In zone coverages, you can leverage the athleticism of a superior athlete to react to a blocked defender. In the option, since the offense is essentially choosing to leave one player unblocked in order to create the hole to run in, you have an extra blocker to negate the athleticism advantage of a more talented defense. Hence the importance of playing "assignment" football. I'm sure
@ilovetheoption could explain this better than I just did.
FWIW, I think maybe you're conflating "coverage", meaning the positioning used by a defense to defend the field with "assignments", which are the individual instructions and responsibilities given to each player.
Most coaches I know prefer to play more zone coverage against the option, just because it means you don't have guys turning their backs and chasing blockers downfield. Doing that means you've made their block for them, rather than at least having a chance to beat the block and rally to the ball to gain a tackler.
An old offensive coordinator I knew liked to say that he ran just as much option as he needed to keep the defense in zone, because his whole passing game was zone-beaters.
Honestly I think the "assignment football" thing is sort of announcer-speak meaning mostly nothing. I have always read it pretty much as
@85Escape does. Against most teams that are trying to leverage doubleteams and just slam the living hell out of the B gaps, you want guys fighting off their blocks and flying to the ball, and if they're a little bit out of control, honestly that's okay. The whole "spill and kill" mantra that defensive coordinators preach (particular your Tite front guys) is clogging up the middle, and then let everybody else rally to the ball before it gets upfield.
Against a PJ style option offense, that's not what you want. If they don't block you, that's fine, you do your job. Don't worry about rallying to the ball, don't try to make a big play. Tackle the guy you're supposed to tackle, and you'll have done your job. Particularly in your front 5/6. Make the boring play.
That's so opposed to how teams normally play that they get it wrong. Either they stay too aggressive, or they tone it down too far and get passive. That's what I think it's about. It's hard to dial it back the exact right amount when you haven't done it since you were a sophomore in High School.