According to what Timex says, the answer is quite simple. When the time is fixed at 10:10, it gives the look of a 'smile' and the manufacturers want their products to be smiling at the customers. Another advantage is that in that position, the manufacturers' trademark or logo on the top of the dial is fully visible. Timex clocks always show exactly 10:09:36 in their ads. Later this became a custom to show 10:10 on all watches, and even digital watches show this time.
But it should be noted that there do are some companies whose watches show other times such as 08:20.