Here is another idea that would greatly assist Rohan late game, while also giving incentive to change from Peasant spam to Cavalry late game. This idea is fairly simple, and very fair and not overpowered in my opinion. It would also be exceedingly easy to implement.
Add a new unit to the Assembly Point, essentially the herald from 3.8.1. This unit has 2 requirements that must be met before they can be recruited. First, all 3 of the captains of Rohan must be recruited(Elfhelm, Erkenbrand, Grimbold), and second, Théoden must be cured of Grima's corruption. The units themselves would be elite cavalry, who do not grant any leaderships and have no formations, but have the passive ability "Elite Cavalry Training" which causes them to passively take only half damage from pikes. These units should cost 500 resources and 90 CP each, and be able to receive upgrades and level up. They should also not receive the discount from the Stud Farms, and should always cost 500.
This would fill the gap Rohan currently has for elite units(not hero units), with the only real elite unit currently being the Rohirrim Archers, and also give Rohan a strong cavalry unit for late game that could still be killed, but at least would stand a fighting chance. It would also prevent them from being OP early game, because you need to cure Théoden and get all 3 of the other captains from the Assembly Point first, and they are fairly expensive at 500 resources and 90 CP. You could just use the current Westfold Cavalry unit summoned by Erkenbrand in his cavalry form, and since its the only unit that Erkenbrand can summon that lacks a formation/ability, I think the passive reduction to pike damage would fit very well, and not be OP. Finally, this would fit extremely well for Rohan being a cavalry faction, and would add a lot of incentive for players to switch from the current peasant spam all game to using cavalry late game.
Finally, I am well aware of how effective Rohirrim Archers are at killing pikes and heavily armored units, but they are also EXTREMELY weak against archers. All you need to counter them is 3 units of archers with fire arrows, or 3 crossbowmen with steel bolts, and you can deal serious damage to an army of Rohirrim Archers.