How necessary are perimieter lines? I don't think they really fit well with the style of the kayak.

I really think that perimeter lines are essential safety equipment on sea kayaks.
I won't paddle a sea kayak without them, and if I have the option, I won't paddle with anybody else whose boat doesn't have perimeter lines.
It is really, really difficult to maneuver a boat without perimeter lines if you are doing a rescue, or even 'rafting up'.

If you have a few minutes, watch this video ('My First Rescue') of two boats without perimeter lines, especially the part around the 4 minute mark.
http://www.youtube.com/watch?v=akdymHzO4So

And, it's a lot tougher if it's a situation where one boat is upside down and you need to grab it.

'Regulars' here at kayakforum will be tired of my rants on this ;-) but I'm amazed at the number of 'woodcrafty' sea kayaks you can see in web pictures that don't have perimeter lines (or safe end toggles).