Deep fakes lack context. There are no witnesses, etc. So they’ll be most “effective” in trying to establish something in the past. It’ll be harder to produce the context where it’s believable in the near past (present minus up to a day a month a year?). So they may be useful in sowing distrust in someone by establishing they did something untoward in the past, but less likely to incite immediate reaction about something happening now, or recent past, once people become used to the possibility.
People already remember things that didn't happen; and public figures already get maligned by news outlets lying about what they did and where they went. Even when the situations are revealed to be lies.