On Mon, 15 May 2017 08:23:09 -0700 (PDT), robobass
wrote:

1: Do you really use a 14mm socket?

Yes

Do you actually encounter 14mm hex heads?

Yes

Give me one example.

Both rear engine mounting bolts on my bike. (Yamaha FJR)

14mm isn't uncommon. Here are a couple.
https://www.fastenal.com/products/details/11120395
http://www.ebay.com/itm/Banjo-bolt-w...W76 O&vxp=mtr

And you'll find it here in the JIS column.
http://www.engineeringtoolbox.com/me...ze-d_1458.html