Not all travel agencies abroad selling the JR Pass would understand the details (and perhaps just a few of them have actually used the pass for travels). You can always reserve seats with the Pass (unless the seats are fully booked). However, it's also true that if you take the train from the departing train terminal the non-reserved sections of the train sets won't be fully occupied (unless on a busy day and hour). That said, it only takes a few minutes to reserve seats at the ticket office (unless there is big line during the peak hours), and as you can book it well in advance and up to a minute before departure, there is no reason why you shouldn't.
While the Shinkansen has same seats for both reserved and non-reserved sections of the car, on some limited express trains in the rural areas the trains have better seats in the reserved section.
Hikari trains would be rarely full, as the overwhelming majority of passengers take the Nozomi, which runs at 10-15 min intervals per hour, stopping at limited number of stations (after leaving Shinagawa in Tokyo, they just stop at Shin-Yokohama, Nagoya, Kyoto before arriving at Osaka).
Edited: 3:46 am, May 13, 2013