Weighing in on this, the stable requirement for mounting at this point is, in my opinion, a leftover of 3.8.1 and an unnecessary gimmick.
It has never directly hurt my gameplay in any ways I can think of, but just on the pure fact of how many other factions get heroes who can mount, having only Rohan locked off by the stables actually makes about as little sense as it can make.
As you said Die, Rohan is a cavalry faction, they are the Horse Lords, and so why shouldn't their heroes have their mounts available freely? Lets do a quick comparison:
Rohan: 6 heroes who can mount and their hobbit, 7 total heroes.
Gondor: 4 heroes who can mount, 8 heroes total.
Mordor: 7 heroes who can mount counting black rider battalion, 9 heroes total.
Imladris: 3 heroes that can mount, 7 heroes total.
So with the available factions who have more than a single mounted hero, we see the majority have at least half of their available heroes as mountable heroes, with no restrictions at all except in Gondors case concerning levelling up the heroes. If you want to mount up Gandalf having never built a stables, you can go right ahead. Now obviously Mordor doesn't have a stables, but the point still stands for them as well. Finally, for Imladris, half of their heroes can mount and provide support to their already excellent cavalry, or just mount to escape from battle, no restrictions.
I can see no reason to retain this unnecessary restriction. All it really does is hurt gameplay, for example if you are doing an infantry strategy as Rohan(which is necessary much more often than you may think) and never make a stables, focusing instead on an Archery Range, you have literally no ability to mount your hero, whether it be to get them to the frontline or escape when close to death. It is, at the end of the day, a hindrance more than a feature.