I've made posts about this before, but after this latest episode I think it's fair to discuss this on its own. Trek has depicted Federation/Starfleet leaders in the past. Rillak might be the best of the bunch. Admittedly, the standard hasn't always been very high, as a lot of those leaders were written to be shallow, incompetent, easily manipulated, manipulative, selfish, evil, and/or weak. Rillak is a interesting case though. While clearly a politician first, she's not stereotypically conniving or selfish. And while she's true to the cause of furthering the Federation's ideals, she's not completely altruistic or heroic either. She's simply well-written in the sense that the writers have decided to make her character more complex than your standard good or evil leader. She's politically savvy, but mostly honest about her politics to Burnham. She doesn't always make the most popular decisions, but she's competent and believes in what the Federation stands for. She's no pushover when it comes to being pressured, but she knows when to delegate and trust others to do what is needed. It's a relief to have two leaders (Vance is the other one) written to be capable and complex, but not bereft of morals. Rillak's performance at the assembly was a masterclass in politics and leadership. If the Federation was a real thing, I'd feel pretty good about having someone like Rillak in charge.
Honestly, she strikes me as generic politician/authority figure. The actress is doing a decent job making an engaging enough character out of what's given to her, and indeed that's largely the case with pretty much everyone on the show, what perceived depth they have has more to do with the actors playing the roles than with how they're written. Even Admiral Vance's appeal has more to do with Oded Fehr's portrayal than how he's written.
I don't particularly like her. She uses Burnham to do all the work for her. Might as well make Michael president.
All the work that we see Rillak delegate to Burnham, that is. Which is not all the work that needs doing to govern a Federation.
If Burnham screws up, Rillak has someone to throw under the bus. Plus, by keeping Burnham close, Rillak is keeping her under control. Burnham's no politician; but Rillak is a politician through and through. What I like better about Rillak than Kai Winn is that Rillak isn't being written as an antagonist. That would've been too easy.
I disagree. I think the best leader we've seen is Hiram Roth (the president from ST IV). I mean, I have nothing really against Rillak, but I agree with @Unionized Elf - she's more of your typical politician who waffles and makes compromises. Roth didn't strike me that way at all. Admitedly, we've seen much more of Rillak in action than we have Roth, but there we are. And no, I'm not putting Rillak down because she's a woman or anything like that. It's just that...Rillak is such a typical politician, sometimes she just sounds like she's reading from a TelePrompTer. Roth just gets shit done.
I mean... Roth wasn't really much of a character though. He was a guy who's more a plot device than anything else -- he presides over Kirk and company's court-martial, he warns people away from Earth, and then he smiles and tells Kirk that basically all is forgiven and he gets to be a starship captain again. To be frank, all of the Federation Presidents we have seen up until now have been basically plot devices without much depth. Ra-ghoratreii (the President in TUC) was there to look pensive about not rescuing Kirk from the Klingons and then to be saved by Kirk at the end; Jaresh-Inyo was there to be tricked by Leyton. The only President who wasn't a cardboard cut-out until now was Archer from ENT, and that doesn't count because no one knew he was gonna be Federation President until Mike Sussman stuck it on a viewscreen in post-production of "In A Mirror, Darkly, Part II!" I like Rillak and think she's the first canonical Federation President with much in the way of depth or personality. (I still prefer Nan Bacco from the novels, but whachagonnado?)