I have a /48 that I can basically roll through.

A /64 is more than enough though to prevent most casual attempts at entry; and does force more work / enumeration to be done to break into a network and do damage with. I'm not saying the privacy extensions are the greatest; but they do work to slightly increase the difficulty of tracking and exploitation.

With a /48 or even a /56; I can subdivide things and hand out several /64s to each device too; which would shake up things if tracking expects a /64 explicitly.

I actually use /55s to cordon off blocks inside the /48 that aren't used too. So dialing a random prefix won't help. You'd be surprised how often I get intrusive portsweeps trying to enumerate my /64s this way...and it doesn't work because I'm not subnetting on any standard behavior.