The real reason for the setting? Aesthetics. The 10:10 position gives the clock or watch a number of benefits:
• The hands not overlapping, so they’re fully and clearly visible and their styling can be admired.
• The arrangement of the hands is symmetrical, which people generally find more pleasant than asymmetry, making the product more appealing to customers.
• The manufacturer’s logo, usually in the center of the face under the 12, is not only visible, but nicely framed by the hands.
• Additional elements on the face (like date windows and secondary dials), usually placed near the 3, 6, or 9, won’t be obscured.
According to the folks at Timex (who set their products at 10:09:36 exactly), the standard setting used to be 8:20, but this made the face look like it was frowning. To make the products look “happier,” the setting was flipped into a smile (occasionally, you’ll still see the 8:20 setting on some clocks or watches where the manufacturer’s logo is at bottom of the face above the 6).