I agree with your broader point - that the game heavily encourages 'optimized' runs, and that it can be a struggle to justify picking up some of the more obscure skills and quests. I'd have to respectfully disagree on some of the specifics you bring up.
For example: there are a few interactions that get locked behind having an elector's background investigated. I felt the same way you did when I first played - I would savescum to see if I could get a blackmail hook or a proposal out of the background, and revert to the old save if I got neither. But everything changed when I did my 100 Intrigue run. The primary impact seems to be flavor text, but just off the top of my head: Chapadoc unlocks an entirely new option for her quest if you go into it with her background investigated. Her usual quest tests Big Guns, which is a deeply useless skill that I've never been incentivized to pick up. Her other option is not only hilarious, but it's also solvable with a wide range of skills.
I definitely wouldn't say no to having some additional incentives to properly investigate backgrounds, though.
I also think you've written off Heru IV way too quickly - it sounds like you had a pretty bad first run with them, because 2 out of the 3 electors start off with really high approval for you. The 3rd one isn't extremely negative either. Obviously they can turn on you, like you experienced, if you make choices which anger them, but you really shouldn't write off the entire faction. Grojdana is the best advisor in the game IMO, Jade has some good stats and a quest you can auto-win with a good science advisor, and Rippling Eternity provides insight into some Heru politics. If any faction feels a bit unfair to me, I'd say it's Heru II - I feel like I can only get Khdarr's approval if I'm planning a run around it.
In my perfect world, I do wish that the specific advisors you hired could have a wider impact on the story. There's one instance where having Sola as your advisor can give you a new choice in the main story, and I'd love more like that. I'd also love the ability to get to talk with your advisors in deep space. I've dug around this game as much as I could and I still haven't gotten my definitive answers on how Eve & Vahter knew our mom, the Branekka-Milan beef, and plenty other mini mysteries. I'd die for some more hints on that. And for some more interactions with our marriage partners!
I say in my perfect world, because, well... given the amount of choice in this game, I don't know how feasible such a thing would be. My gut says it'd be a logistical nightmare. But I do miss the one-on-one interactions you could get in LLTQ - like helping Adair catch frogs in the courtyard and talking with Charlotte when she first comes to visit.
Just to throw some ideas out there - even though we're given a lot of choice about where we assign electors in our cabinet, there are clearly some roles that they are best equipped to fill. So maybe they could have one special event based on that? Like, okay, Stoyan just got done advising me on science, and now there's a brief scene you can view in deep space where you have a chat with him, learn a bit more about his deal, and maybe gain a +5 to a stat.