Designated Survivor is an interesting version of a decent concept, with strong characters and a decent plot. From the start it's run as two storylines running alongside each other: President Tom Kirkman's attempt to navigate politics as someone with little political ambition or experience, and FBI agent Hannah Wells' attempt to track down the people behind the attack. The first series does a good job building on these, showing Kirkman's attempt to rebuild the US government and Wells' spy plot.
The second series is broadly the same, introducing a few new characters and building well on the existing ones. Kirkman's movement through politics transitions from rebuilding the country to operating normally and exploring the problems he has moving through the system. Hannah has two distinct arcs over the series the first wrapping up some threads from the first series and the second revolving around a plot of double agents. This series feels like the strongest of the three, the characters interact more easily and naturally although the main plot feels slightly less connected. Kirkman's plot tends to hover primarily around a single issue that's brought up and resolved over only one or two episodes, as opposed to the first where the story carries over the entire series.
Series three was taken over by Netflix, and the dropping of some characters is kind of a shame. The series also uses clips of people speaking about real world experiences, which is an interesting concept but I feel wasn't integrated into the show as well as I'd like. The first half falls into the same issues as the second series with each episode having a separate issue it introduces then resolves within the 50 minute runtime. It's interesting to see Kirkman's transition from public servant to politician over the series, although the last episode feels like it doesn't fully resolve this or some other character arcs.
Individually the characters are mostly great, although the antagonists often feel a little underdeveloped, especially in the second and third series. Kal Penn is fantastic as Seth Wright, and he has fantastic chemistry with Paulo Constanzo (Lyor Boone) in the second series. Sashsa feels slightly underdeveloped and feels a bit like she comes out of nowhere, she's well acted and pretty good when she's onscreen, but feels like she got less development than the other characters. Leo's not in it that much, is underdeveloped in the first two series and absent from the third. When he's there, he's great, but his story doesn't get nearly enough attention and threads get dropped without much acknowledgement.
It's maintained throughout the entirety of the show that Kirkman's a centrist, but honestly he feels like a liberal. I don't mean this as a dig against him or the show, but it's clear that his policies are left wing and the show would've been stronger if it had been comfortable with admitting that. He wouldn't even have to be a Dem, his policies definitely feel different to theirs in a few ways, but he's definitely not a centrist.
The second and third series definitely also comment on politics as it exists today, but it does so in a decent way. Some of the allegory is fairly transparent (in the second series there's a threat of war between to bordering Asian nations who were once one country, and the US has to help negotiate a peace treaty) but serves its purpose well. Again, the politics is definitely left of centre, but isn't particularly radical and makes sense in the context of a show about the president.