The Civ 3 mods CCM1, CCM 2 and now CCM 3 show since more than a decade, that different leaders for different eras can work very well. The nonsense with the immortal leader who is coming with the start of a game - and therefore mostly even in the scale of time completely wrong - is not needed any longer. Think of the civs as the people, who are living in a certain geographic space of earth. Therefore in CCM you have civs like Maghreb (consisting of Carthage in era 1, the Berbers in era 2, Maghreb in era 3 and 4), Scandinavia, Indochina, a civ Rome/Italian city states/ Italy and so on. Argumentations in the Civ 7 threads, that civs were conquered, per example Egypt, loose their weight when the civs are the people, who are living in that "conquered" part of the earth (in the animation below you can see, that the leader for Egypt in era 2 is the Sultan Baibars). The people in the same geographic space nearly mostly were melting together.
The new Civ 3 mod C3X by Flintlock even offers the options to give those civs and their era-specific leaders different era-specific names and titles.
You can read more about the multiple leader system in CCM
here. Here is an animation about eight of the era-specific civs and leaders in CCM 3. CCM3 holds 31 era-specific civs and their leaders. Different to Civ 7, Civ 3 holds four eras. The multiple leaders in CCM 3 are limited to the available leaders for modding Civ 3 and in some cases CCM 3 uses iconic leaders of "neighbouring" eras or the first existing iconic leader of a civ, even if that leader was living in a later era (per example for the USA which are a special case).
A special version of this mod, giving those era-specific leaders a kind of an "individual personality" by special great wonders, which can be created by the civ in that special era, is in work.
How much better can this be done by Firaxis themselves, without the limitations that a simple Civ 3 modder has to respect (per example only 256 buildings in a Civ 3 game).
Edit 25.08.24: I changed my vote as I strongly liked to play a civ with different leaders in different eras (as shown above) and now it seems that one should keep a leader and play different civs in different eras - a setting that I don´t like.