1) The hero must be self-sufficient.
2) Have an incentive for development.
3) Ability to be the main hero among others.
Indirect:
4) Good synergy.
5) Simplicity and uniqueness of the special ability.

The proposed special abilities for improving mines/capturing mines lack clear, essential points.

It's not that simple: you come up with something and just add it in. Even Eymund, who uses mines like dwellings for Bone Collectors, doesn't appeal to me much, even though he brings something good to the game. In the future, I even want to simplify it so that he "simply" turns mines into dwellings, with the increase depending on the hero's level and/or the more mines converted, the greater the bonus (parameter).

Thus, the hero will be able to deprive the enemy of a necessary resource permanently in a particular game. The transformation will, of course, cost money, and the higher the hero's level, the less gold will be required.
It would be interesting to have different army units generated in different mines: for example, a crystal mine produces two Tians per week, and a gem mine produces four Priests per week.

Added 22 minutes later
Eymund

Starting Machines
Completed Rune
Earthquake
Ballista, Cart
Engineer
The hero converts any mines into creature dwellings (basic weekly increases: crystals - Tians, gems - Elders, stone - Shields, wood - Spears, sulfur - Bears, Bone Collectors - Mercury, Dragons - Gold). The transformation is possible if the hero's level is not less than (week * 4).