Interesting. I like how you combined two rather divergent opinions and think you're on to something. I would like to see the implementation go a different direction though...I would be fine with having Leader and Leader abilities work just like Governors. I would make Leaders and Governors share promotions because I think it would help alleviate the problem @ShakaKhan points out. If a Leader doesn't have early abilities you can promote governors instead. That also means you could give players the option of choosing a new Leader at the cost of loosing the promotions the old one had.
First, some preamble on my thoughts on leaders and governors. I have no problem with the immortal leader suspension-of-disbelief, but I think the impact of leaders could use some retooling - the fact that the civilization grants three abilities to your game whereas the leader provides one seems to make the leader less important than the civilization of choice. Also, when you look at the initial release, it seemed that they wanted to provide the "player choices," meaning the combination of civilization/leader that they chose, have 4 abilities/bonuses and it was not really important whether the bonus came from the leader or the civilization. Some "player choices" had two strong bonuses and two weak ones, and whether it was two strong civilization abilities or one strong civilization ability and one strong leader ability didn't really matter. The litmus test for this was Greece, the only civilization that had two leaders upon release, and I will admit that Gorgo and Pericles had very different bonuses that did lend themselves better to different styles of play, but still, if you were playing Greece, your strategy was to utilize the extra wildcard slot {which can be leveraged any way you wanted, really one of the best general bonuses to get) along with a decent and very early UU, with the other two bonuses, regardless of which leader you chose, benefiting culture, which gave them an inclination towards that victory regardless of which leader you chose. Now Eleanora did show us how having a leader for two different civilizations is implemented quite differently. As for governors...
...With Rise and Fall, governors had bonuses that, for the most part, only affected the city that they were governing in. While you can move them around, you lost some efficiency of the governor when doing so as it takes some turns for them to relocate. The fact that they only affected the city that they were in, to me, seemed to be a move towards making tall empires more of a viable choice. The problem with that is that whether your civilization had 4 cities or 30, you ended up with the same amount of governors (well, governor promotions.) And while the immortal leader suspension-of-disbelief didn't bother me, it does bother me a little with governors, as there are 5 civilizations in the world, and among them, there's a Chinese Pingala, a Korean Pingala, a Roman Pingala, and an American Pingala. And then there's a Korean Magnus, a Roman Magnus, and a Mongolian Magnus... And so on.
So back to my preference in how to implement your idea. Rather than having leaders and governors continue as two separate game mechanics where they share promotions, and having early civs developing their leaders while more modern civs focus on their governors, I would combine the two mechanics - basically instead of leaders giving a bonus that impacts your whole civilization (and being only 1/4 of the civ-wide bonuses that your civilization/leader choice grants you) while governors provide significant bonuses but only to the city that they are in... instead of that I'm proposing instead of having seperate game mechanics of leaders and governors you have a shared game mechanic of a leader and his cabinet. For the leader bonuses, go back to the best entry in the franchise, civ4, where they give a combination of 2 out of 10 (or 3 out of 10, keep things progressive) traits that each are strong in their own right and yet are utilized differently based on how they synergize with each other. and you can continue to promote/develop this leader to have more pronounced advantages with those three traits...OR... in lieu of developing this leader to reach his/her full potential, you could add more members to the cabinet of the leader (we'll call them senators for now) and there are 4 or 5 categories of possible senators to fill your cabinet with, each category containing several options that are mutually exclusive. For example, from one category you could chose one of four senators, one that gives bonuses to hilly/mountainous cities, one that gives bonuses to flatland/hilly cities, one that gives bonuses to coastal cities, and one that gives bonuses to desert and tundra cities. Another category of senators would have one that gives moderate combat bonuses, one that gives moderate economic bonuses, one that gives weaker research bonuses, and one that gives moderate culture and religious bonuses. And possibly the most important category of senators is the one that the game uses as an "equalizer" for the other game mechanics it introduces. You have one senator category that has two choices - one senator that maximizes the advantages of a tall empire, and the other senator choice that maximizes the advantages of a wide empire. And as time progresses, the DLC changes the advatages so that if this new game plays like Civ5, where tall empires are clearly better than wide empires, the "tall governor" has less powerful advantages while the "wide governor" gets more potent advantages, and vice-versa if the game seems to be more like civ6 where wide empires are better than tall ones.