I’ve seen a few stallions, some from very well known breeding operations that are described as siring both hunter and dressage offspring. These disciplines require very different types of movement, so why are some of these stallions being promoted for both?
You can get a nice enough hunter from some of the dressage stallions. Training methods can make the trot a bit more huntery and many of those dressage stallions have lovely temperaments. Plenty athletic for your average 3’ hunter. I’m always surprised when I see 3* event horses with more dresssge lines (RF Demeter the perfect example), or a Jersey Botmy, but some of their stallion testing scores are decent enough for jumping & they are trainable enough to succeed in the h/I ring.
I think there are two different types of dressage stallions that get recommended - some are dressage horses from jumping lines/pedigrees that still have some influence from those horses (Sandro Song, Pik As are both examples - so the S line horses and some of the ones that have Pik As closer up). That’s where I see sense in some of the Sandro Hit sons being suggested, and many of the D line stallions that get suggested (although there aren’t too many of these, admittedly) tend to be the Donnerhall sons out of Pik Bube mares.
The other ones that I see (and these are more common - the R horses, particularly) are the horses that have fundamentally good gaits. Many of the R stallions are notable for just the bare excellence of the paces - the rhythm is natural and good, the mechanics aren’t necessarily wildly flashy (“modern”) but they use themselves well front to back and have a reputation for relaxation and working over their back. For the R horses to succeed in dressage breeding, you see them paired with horses that can either drive more from behind or lift more in front to help with the bigger gaits that are more popular - but for hunter breeding, I think that the basic quality of their movement stands on its own. Royal Prince is one still standing that comes to mind for this.