He will likely stay sound for lower levels of dressage. Most any horse will.. and, IMO, be better able to stay soound because dressage teaches a horse how to use his body.
Your horse has a nice topline and a very short back but he is built downhill and that will make it difficult for him to lighten his forehand and shift his weight to the rear. He CAN do it, but it will take more effort on his part. He is also quite sickle hocked.
I suspect the reason he runs thru the bridle when he canters is due to lack of balance and an inability to shift his weight to the rear easily with a rider on top. Remember.. you sit on a horse and basic physics changes everything for him.
In the photo of your riding him at the walk with his head low he is clearly being ridden front to back. He needs to be driven forward and asked to shift his weight to the rear. This is riding back to front and opposite of that photo.
Being broken to saddle as a three year old is not any sort of set back. In fact, a lot of warmbloods are not ridden until 3 or 4. The age should make no difference. OTOH, HOW he is broken to saddle is where the issues can begin.
I suggest you read this site. What does 'on the bit' really mean?
Your horse is a good one and can be trained and should be trained but he will need to learn to use his ring of muscles and you will need to learn to ride him so he does.
Good luck. He is a decent little horse.