A one word answer : tradition and custom.
In Andalucia in Southern Spain, horse riding is largely a male dominated sport - even a culture. The men do not like to be seen riding anything else other than a flashy - often beautiful, stallion. Spanish men love to parade their horses.
If you visit the country fairs you will see milling about in the town square lots of well groomed, impeccably behaved, stallions ridden by some very well dressed men. Often there is a very traditionally dressed senora or senorita sitting up behind - sidesaddle.
A feria (fair) is without a doubt a fantastic sight and well worth seeing.
However one mare in season can cause havoc amongst the stallions. And so as to avoid problems in a crowded environment the men say: "stallions only".
At the bigger studs, mares are very often kept in a big communial paddock along with the youngstock. The stallions, and there can be a hundred, each have their own large stables. The stable grooms are invariably men.
In Britain - it is exactly the opposite - here this female dominated society says that stallions represent a hazard at the horse shows where there will be lots of ridden mares (some in season) - so almost invariably all colts are gelded at a young age unless there are plans to keep them for breeding.
It is the same fundamental problem of maintaining control- ie over excitement- but the Spaniards don't believe in the castration of a good horse, they believe only an entire horse has "spirit".
When the British go and live in Spain, they buy the mares and they have them schooled to ride. Schooling represents no more a problem than with any other breed of mare. But folks I know say that it is always best to school an Andalucian horse the Spanish way - which can be a bit harsh by British standards. The results can be spectacular and a well schooled, fancily bred Andalucian horse is a delight to ride. I can vouch for that.
It is also a breed well conditioned to living in a hot dry climate.
I'd love to own one but perhaps the grass is too rich and green where I live. They are also very expensive to buy. The really good ones rarely leave Spain. There is a tangled web of paperwork to follow to get an export licence for a well bred stallion.
Put that mare to stud but only to an Andalucian stallion
Or just maybe a Lusitano or perhaps a Lippizaner - dreams!!!!
My DiDi is the closest thing to a Lusitano which I could afford ( PS for "Lusitano" read "Portuguese Andalucian")