I really like the idea of making leaders less "specialised", and more representative of the heads of particular departments / institutions.
Your civics, ethics and the way you've built your worlds (ratio of types of buildings / districts / jobs) should provide the basis for the generation of your leader pool. Your leaders are not specialised initially, but can become specialised over time.
Based on your civics, you start with a basic number of "institutions". Some of these institutions sit within government, and are therefore under your control, and some don't, and aren't.
So, let's say you're a Materialist, Xenophile Democracy. You'll start with some institutions representing the basic structure of your Government: research departments, a xeno first contact department, a diplomatic corps, maybe. You have a leader pool and you can assign them to these various departments. There are not separate types of leaders, the only thing that differentiates them is their traits.
Leaders will develop traits over time weighted randomly and by the institution they are assigned to. So, you pick a leader with a military background and you assign them to head the physics department. You're more likely to pull weapons-related tech, and you'll get appropriate bonuses based on that. That leader also has a set of ethics, and since they are a generic leader, they can potentially become your Ruler too. The traits they've accrued over their career so far (based on where you've assigned them) will carry over into their Rulership. This seems better to me as currently you have specific "scientist" characters that often become President in your democracy... this strikes me as odd, how many scientists generally jump from an academic career to politics, and then back again?
You'll also unlock more institutions as you play through the game, probably via tech, and maybe certain requirements like needing a certain number of jobs of a particular type or something like that. There's some precedent for institutions kinda already (ie. the Bureau of Espionage edict).
The thing I like about this is you get a huge amount of freedom to define what your empire is actually like, based on the institutions and leaders you cultivate. The way you build your worlds affects the leaders you get, and the institutions you define allows you to mix and match what you do with them.
So maybe I go heavy on military with the institutions, but I create a lot of commercially-focused worlds. I end up with an empire that's essentially a military-industrial complex, where I have leaders with business / economy-type traits running military institutions and providing unique bonuses to my empire based on that, maybe lower ship upkeep and ship build cost. Or, maybe vice versa, I go for a lot of commercial institutions, but with a lot of stronghold / military academy worlds. So I have an economically-focused set of institutions but with leaders cultivated with military backgrounds. This could provide bonuses like bonuses to military-related research, alloy production.
The combinations / ability to customise could quite literally be endless. And that's before I even start talking about how this could tie into the factions system. But this post is already long enough.