At least in the case of these strawberries, the answer is no. All alpines are small, the red and white ones don’t really have a size difference.
There are pineberries which are essentially white “modern” strawberries but in reality they haven’t undergone nearly as much breeding and selection for size as their red cousins.
I’d imagine for white blackberries, they found a blackberry plant with the mutation that lead it to become white and then figured that would be enough of a selection difference in and of itself to be sold well by those interested. So they selected for white, not for size.