Well, mechanically, one-handed backhands are very tough on the shoulder.
(The follow through phase of the one-hander is very bad on the shoulder. The shoulder is not as stable when it's raised that high. The supraspinatus tendon of the rotator cuff, along with a sac of lubricating tissue called bursa actually rubs against a bone called acromion. Repetitive irritation can be very painful, this is called impingement syndrome. Further irritation and the bursa becomes useless as a cushion, and the supraspinatus tendon rubs against the acromion bone, eventually the tendon tears away. This is why serves lead to shoulder problems, especially the kick serve.
A strong rotator cuff will prevent such rubbing. Trust me, coming back from torn rotator cuff surgery taught me a lot about the shoulder. I had a partially torn supraspinatus, my bursa was removed because of inflammation and it was basically useless, supraspinatus was repaired. So i have to keep my rotator cuff strong to prevent tearing my surgically repaired supraspinatus again. I was 16 when i had the surgery, i'm 20 now. Made a full recovery but i need to work on my shoulders all the time, to prevent and keep it strong
Sorry for such a long explanation, but it helps my argument)
Tennis lesson usually starts when a person is young, the supporting tendons around the shoulder (rotator cuff) arent strong enough. So it's recommended that kids start with two-handers, they then get so comfortable with it, it's hard for them to change to a one-hander. And in tennis, you stick with what works.
Luckily for me, i was taught one-hander first, two-hander second. And i chose one-hander. It just feels so comfortable. For me, two-hander is the harder of the two shots.