The Doctor has already been through quite a few regenerations, each new body requiring a change in style. The velvet and lace his third body had favoured would have been completely out of place on his ninth. His eighth might have been able to carry off such a flouncy style, he had the hair for it, but the cricket whites of his fifth regeneration would have looked silly on him.
It’s the same with footwear; different feet need different shoes, preferably something he can run in.
The Doctor waggles his new toes. His tenth pair of feet are definitely sneaker-wearers.