If the horses are actively having to avoid stress-causing conflicts, then that would be increasing their stress levels. A mix where one species intentionally has to flee from the other and escape is not a mix that is conducive to success.
Sure, but the space requirement to allow this mix to be successful and relatively stress-free would be substantially higher than what either species individually requires. Places such as The Wilds, SDWAP, etc. that have paddocks of five plus acres may be able to cohabitate these species, but traditional zoos don't have the spatial needs to mix these two species, especially when both would be more stress-free in smaller single-species exhibits.
You're partially correct here. While mixed species exhibits do often lead to increased space for the animals, and oftentimes mixes include species that won't interact much, mixes also need to consider the physical, social, and mental well-beings of the individuals when they do come into contact- as it's inevitable that at some point in time two species sharing an enclosure will come into contact, and oftentimes occurs quite often. Just because a mix can be done without killing anything doesn't make it a good idea.
I still disagree, that a species tends to avoid another doesn't mean it's constantly stressed that conflicts could arise (conflicts being any form of antagonistic behavior between the two species, not the physical type most people think of). That's like pretending people are always going to be stressed when a train passes by, because they would get overrun if they stand on the tracks. Or that many animals living in large herds would continuously be stressed because on of their conspecifics could in theory attack them (intraspecific aggression and murder is way more common than many people would think). Animals learn to deal with the social situation, and if the exhibit and species assemblage allows it they will behave accordingly and stress levels will go down to normal levels. During the introduction fase, when both species are still learning each others behavior, some conflicts might arise and stress levels could be slightly higher for a bit. Hence the need for good introduction procedures, trained staff and the option to separate individuals and even whole species as the need arises.
In reality, in practically every mix animals can hurt each other if they really wanted to. Even in a species-only exhibit. Yet, animals adapt their behavior and learn how to deal with it as long as none of the species/individuals actively seeks out conflicts. And once again, cortisol levels will stabilize and you end up with an assemblage of species with more space and potentially also with positive interspecific interactions than there would have been had the species all been given separate exhibits. And that space certainly doesn't need to be measured in hectares, as shown by exhibits like the savannah of Artis beautifully uses visual barriers and feeding-station placement to create a conflict-light exhibit.
I've also never said that because species don't kill each other, it's a good mix. Such demonstrate many of the other replies I've given on this thread. On the other hand, quick conflicts are also far less problematic than you seem to be making them. What is most problematic is when a species is actively and continuously being harassed by another species. Short, irregular conflicts cause bursts in stress but are not detrimental to the long-term physical health of an animal and could even be considered a form of enrichment. In fact, with elephants that has even been suggested as an important part in increasing their immunotolerance to EEHV and why it seems less prevalent in nature.