What potential injuries can result from putting high arched feet in stability shoes?

Probably none. A stability shoe is one that is made very rigid in the mid-sole area mainly in theory to reduce foot pronation (flattening of the arch). I do not see where this can injure a person with a high arched (supinated) foot structure. High arched individuals ususally have issues with shock absorption and may benefit with otc arch supports or custom orthotics to better distribute stress across the feet.