I'm not a huge fan of the way heroes are currently distributed.  Choosing between 3 heroes who have no thematic reason to exist (ie: from races I've never met) leaves me feeling a bit cold.  I have very little attachment to these "characters" that are almost purely mechanical.

So for my suggestion:

1

I would much prefer if you EARNED a hero through actual gameplay.  So there would be actions that had a certain % chance of generating a hero, modified by if you were currently hero-heavy or hero-light for the current turn.  

Some examples would be things like learning techs (science hero), building improvements (industrialist), fighting battles (admirals), exploring new sectors (explorers), etc...   So if you are fighting lots of battles, you're likely to get warrior heroes instead of bureaucrats. 

These would be tied to events, so, for example:  After a victory over the Cravers you get a little event pop-up where a Craver battle-hero says he was impressed with the way you fight and he'd like to join your forces.  You can either accept, which would increase your hero count and thus decrease your chances to earn future heroes, or decline (possibly having other side-effects if the writer is feeling creative).

2

I would make the heroes a little less spread-out in their ability distributions.  Right now it's kinda bizarre that my badass space pirates are also governors.  Heroes should probably be one or the other, with abilities to match.  Right now you're shooting yourself in the foot if you don't specialize your hero, making the fact that it has two entirely separate ability trees rather pointless.  I'm not putting any war abilities on my governors, nor FIDSI abilities on my admirals.

3

Each hero could get a small quest-line. 

I've noticed each hero gets a bonus that is unconnected to his ability tree.  I think it would be cool if instead of getting that for free, it was tied to a small quest.  And then a second ability would be unlocked after a harder one.  So continuing our earlier example with the Craver:  Upon hiring, you get a quest goal for him to be victorious in 3 combats.  Upon completion, he gets a bonus for for fleet damage and unlocks a harder, step2 for the quest like defeating a fleet with 8 ships.

The idea here is to create stories with our heroes rather than having them be such dry mechanical elements.  I could also see interesting governor events happening during those events with inter-faction strife.  The industralists and the pacifists are having a power-struggle and when you pick sides, you can install a governor of that faction.

The only time choosing between 3 random heroes makes sense would be if you actually traveled to the Hero Academy and wanted to hire one like a mercenary.

The issue with the first two is it will add even more RNG to a game that is already overly dependent on it. And the last one would be a significant amount of work given the sheer quantity of heroes. The only "fix" the heroes need is more specialization (Switching fleet bonuses for system ones for administrators, and getting rid of system bonuses for fleet-leaders).