What makes Ryshadium special?

[hoser]

When Shallan attends the meeting with the Highprinces, she comments that Hatham is the leader of the largest faction, those trying to reconcile and get everybody to work together.  He basically seems to be between the worlds: somewhat corrupt in a standard Alethi way, but significantly more constructive than most.  Without the "divine" assistance of Dalinar's visions and (what I consider) the divinely inspired hatefulness of Sadeas, finding a way for the highprinces to work together would likely seem the most helpful course.  I could easily see Hatham becoming a Radiant if he survives long enough.

 

I really like the idea presented below, but the textual evidence in the books seems to overrule it. 

...Maybe Ryshadium started off as horses originally, but due to the depth of care shown by their owners, they become something more.  Similar to how a puppy starts off as a normal dog, but eventually becomes a loyal companion who will be there for you through anything.  Dalinar and Adolin seem to genuinely love their horses and you can see it in the way that they care for them.  Out of all of the people in the books, only Adolin and Dalinar seem to care for their horses.  These horses respond to this and start to see themselves as THEIR horses.  Since Adolin and Dalinar see themselves as warriors, their horses see them as warhorses.  This leads to a deepening bond, which allows the horses to siphon sentience (and investiture) off of their riders, allowing them to change.

...

The books seem clear that the Ryshadium are different from the get-go and choose the rider based on some quality which may be related to Radiant predisposition.  It will be interesting to see what happens if Kaladin goes to the Ryshadium place before Odium's minions wipe the Ryshadium out (or try to).  The quote below is one example. 

 

Elhokar’s stallion was a good breed, but it could never match Gallant, who was a full Ryshadium, two hands taller and much stronger than an ordinary horse. The animals chose their own riders, ...

Sanderson, Brandon (2010-08-31). The Way of Kings (The Stormlight Archive) (p. 187). Tom Doherty Associates. Kindle Edition.

If the person and the way they cared was what changed a regular horse into a Ryshadium, then the concept of a "full" Ryshadium wouldn't make any sense, as it seems to be a breeding reference.  It does suggest that there are part-Ryshadiums, which is an interesting concept.