I feel like I should follow what I said with a little explanation about what exactly an EP does. It's a title that gets thrown around a lot, and covers a lot of different things. I'm EP on a movie and all I did was give them story notes. It really depends on the production, size of said production, etc.
Working at the Spielberg level though is a different animal. The guy has pretty much had a studio deal his entire career. So he's never had a need for a producer to find him money. With most studio films, they actually start with the EP developing the concept with a writer and hiring the director when they feel it is ready. In case of the Spielberg, they developed his myriad ideas in the early Amblin days-- finding writers and directors for the projects he wanted to develop on the side versus the ones he was going to direct himself.
Any classic Amblin film produced by Spielberg, Marshal, and Kennedy but directed by somebody else (Gremlins, Goonies, arguably Poltergeist, to name a few) had the three of them involved early on making creative decisions. Development is generally the EPs and the writer having a writer's room to develop the concept. If you want a really cool example of this, search for the Raiders of the Lost Ark story session transcripts. It's Spielberg, Lucas, and Kasdan sitting in a room pitching each other ideas.
So when you're talking about Amblin/Spielberg films in general, some of the most high-concept creative films ever made, I can promise you, Kennedy was involved in the creative aspects of it. Then there's all the physical production aspects-- finding crew, securing locations, planning the budget, arranging for pretty much anything that goes before the camera, making schedules-- there are lower ranking producers whose job is to do these things-- but in the early planning stages, it falls on the EPs until they hire for those positions.
And that's just pre-production. When the movies are shooting, think of the entire production like a company. Everyone answers to somebody above them, up the chain, to a department head. The DP, the First AD, the Key Grip, head of transpo, stunt supervisor, FX supervisor-- etc. Think of department heads as VPs in a company, running different divisions. Above the VPs you'll have the executives. The Director is the President-- the one in charge of all final decisions key to the business. The one running the VPs, and calling shots. The President is in a checks and balances system with the CFO, (an EP); the CEO (another EP), and possible even other "chief" positions.
On a normal production, the EP hires the director for a project, and can fire them. Spielberg's films were ones he brought them to-- but if Spielberg ever went over-time, or over-budget, or was otherwise not doing his job correctly, Kennedy and Marshal would be the ones to tell him and get him back on track.
On-set during the production, the director needs to be able to just focus on what's on his plate for the day-- shooting the scenes on the call sheet. Say it's day 23 of Temple of Doom and they're in the jungle, doing the campfire scene. There's an animal wrangler on set with a cranky bat, you're working night hours meaning people may be getting over-time paychecks cut to them that night, say a suit from Paramount has just arrived to see how things are going and they're a little behind schedule, the elephant wrangler is threatening to walk cause he wants more money, the Indian government is saying they can't use the palace they planned to shoot at anymore cause they don't like how Indian people are being portrayed in the film-- all of that has to be handled in a way that Spielberg is shielded so he can focus and get the scene shot, cause he's got a minor on set who can only work for so many hours.
I made all that up, but that's what could happen on a single day on a big movie, and the person who shields the director and handles this stuff so he can do his job, is one of the EPs. The people who watch the budget and the schedule and keep everything running smoothly-- the EP. They literally run everything.
When you get to post-production the director, especially one like Spielberg, might be ready to bounce onto the next project. Generally the director will over-see editing and FX work being done, but sometimes he can't-- guess who steps in to make the command decisions-- an EP. TRUE story-- Schindler's List came together quick, and Jurassic Park went over-time. Spielberg, Marshal, and Kennedy all had to jump on Schindler while JP was in post. Lucas stepped in as a favor and while he didn't take the credit for it, was essential an EP for JP in post and over-saw most of the post-process.
Anyway-- my point was just that Kennedy was never just an office suit, or somebody who made budgets. She was involved in both the developmental creative, as well as the day to day physical production of some of the biggest movies ever made-- movies made in that same era as the OT and have a very similar feel to them. There are very few people more qualified than her to run Lucasfilm. One may not like her creative direction, but to say she isn't qualified with her experience and resume is preposterous.
THAT said-- she's obviously not infallible. But if we want to critique her, take aim at the legit mistakes she's made. Don't just call her a suit or Disney shill who doesn't know what she's doing. In my eyes, she's really only made one error-- but it's a big one that's been made repeatedly: she's hired the wrong people. Between firings, rewrites, and reshoots, she's chosen the wrong people for the job more than once.
Sure, she couldn't know that Arndt was going to choke, or that Rogue One's first cut might be lacking in some ooomph, or that Trank was going to lose his mind, or that the Solo guys were going to want to improve half the script, or that Treverrow was going to make one of the worst movies ever made... but if it's her job to hire talent, she should have an eye for it. Being a good boss is hiring the right people. I think her heart was in the right place-- to hire a new generation of filmmakers that were raised on Star Wars, but most of them just weren't ready for the scale of things. A good boss should have seen that. Going to Ron Howard was a brilliant move-- he's part of the Lucasfilm family, Lucas mentored him to an extent, he's made a dozen amazing films on his own.
Anyway-- if you hate the creative direction of the Disney era, you could level some of that at her, but just as not-liking TLJ doesn't mean it's a bad movie, not liking her direction doesn't mean she doesn't know what she's doing. There's a difference between an outright mistake, and a choice you just don't like.