Horses are not supposed to be "emotionally available" to us. That's anthropomorphization, projecting human characteristics and needs onto an animal. If he is talented and well trained, that tells me his trainer was sympathetic, skilled and treated him like a horse. Mostly that's a good thing.
That said, I've had horses that disliked being groomed, and disliked human interaction, period, that were, none the less, capable and high performing. You can struggle with this (I had a groom that bought out several tack stores trying to find tools and a grooming routine that would soothe a TB of mine.) or you can accept that it's their nature and their choice. I highly recommend the latter route.
Of my current two horses, one is an affectionate, totally socialized to people, in your pocket cuddle bunny. The other is an aloof, standoffish individual that only enjoys my company when we're out riding; nothing that happens on the ground is interesting or engaging to him. Both are very good horses. I love the fact that the one whinnys at me when he sees me, and comes when I call. But I'm wary of calling that a "bond"; since they're both well trained (frankly, the aloof one is *better* trained); I just accept their individual personalities.
Since you're leasing this horse, learn all you can from him for now. If part of your pleasure in riding is feeling an emotional connection to the horse (you have lots of company in this desire), when you're ready to buy something for your own, absolutely do take that into consideration and find a horse that gratifies you by responding to grooming, affection and treats.