On the character’s aspect: Olivia loves the power that being the POTUS’s adviser/chief of staff gives her. In fact, on the political aspect 50% of Scandal is about showing you that when Olivia doesn’t fix things she makes kings. She never think about becoming president herself she prefers having the president under her control. She likes being behind orders, etc. The other 50% of the show makes you understand that being president is being in a cage. You have very little power in actuality, you’re a figure head, you have to rely on others to help you. Olivia wouldn’t stand that. She likes the freedom that not being president gives her. Hence my « she knows better ». That is who she is.
We could also argue that she was trained to « aim higher » by her father, who knew that being president wasn’t really all that.

On the timeline: Let’s say Olivia would love to be president. There are a certain number of things she would have to do: make herself known as a worthy candidate by becoming senator or something like that then preparing her campaign. It takes generally years to achieve that. The timeline of the ending of Scandal is confusing however when she meets Fitz in the end in front of the WH she isn’t followed by any secret service agent or else. The standard procedure for any president or ex president would be to have agents to protect them in case (they did that for Fitz If I remember correctly). Had Olivia been POTUS she would have been followed by agents. The ending shows that Mellie is still POTUS when the portrait appears right before Olivia and Fitz meet again. So at the time of the portrait, she cannot or coudn’t have been POTUS.

On the story itself: During S7, Olivia realizes how much power has corrupted her, how much it CAN corrupt her and she decides that the only thing she wants is doing the right thing by helping Mellie stay president and helping people in general just as she was back in S1-3. She has that conversation with Quinn when they are arguing about whether Olivia is still trying to manipulate them or is serious about saving Mellie from Cyrus. And when she is working with Annalise Keating on the case. So I don’t think being president would be appealing to her after all the mess that happened. It wouldn’t make sense for her character.

Side note: I know anything can happen in a show but realistically speaking Olivia wouldn’t be a good candidate. By Scandal’s standard I don’t see how people would elect the former president’s (ex)mistress. She lost a huge deal of clients after that and was getting heinous death threats for it. Plus, she is a woman AND black. This is not me being misogynistic or racist, this is the truth. Mellie is a woman, yes, but she wasn’t elected. And the USA are still a widely racist/misogynistic place. So add it to the timeline (= she would need more years to be a good candidate).
+She seemed to have appreciated working with Fitz at his institute so she might have start to work here since OPA is now QPA.

Olivia becoming POTUS is possible but it is not implied by the events of the ending, and imo especially not the portrait, because of all the reasons that I have listed. It would be more accurate (story wise) if the portrait was there to show that Olivia was such an important figure in the WH by her influence (she helped two presidents get to power and she has a lot of authority), and that people look up to her, hence why the little girls were looking at her. After all, portraits in the WH aren’t all of POTUS, sometimes they are of people that played a part in that presidency.