Will I miss cool stuff if I restart?
You can view all the achievements here. There's none related to restarting or not, and I'm 99% percent sure there are no other benefits to a "single life" playthrough.
In fact, it's quite impossible to do a lot of the things in the game without restarting, and designed to be that way. I understand the aspect of wanting to challenge yourself and have a "perfect play", but you'll enjoy yourself much more if you just go with it.
Disclaimer: I worked on Dead Rising 2.