High draft picks always get their playing time, especially when they are considered a "generational talent".
Overall, yes, players selected with the first picks in the draft typically receive a lot of minutes in their debut season, but that's not always the case. Take, for example, Kwame Brown, Anthony Bennett, and Markelle Fultz, who were selected with the first draft picks, but in their debut season, they got few minutes and their performances were very poor, which isn't typical for players selected with the first pick in the draft.
It’s true since it’s always depends on the team they landed. For example Cooper Flagg play under Mavs while the team suffer a lot of injured star players that’s why he is already a perfect fit as starter player to fill his role immediately.
Being drafted by the team with already complete roster like OKC will sure gives you less minutes despite being draft pick since coach will just need to fill few minutes on the player rotation.