At around the same age as your daughter, I was sent to a bad dentist who wouldn't believe me that the novacaine hadn't take effect, that I was in pain, in terrible distress, et cetera. For the next ten years I dealt with terrible dental phobia, to the point that I couldn't smile at myself in a mirror because I'd see my teeth.
Naturally, then, I'm in favor of anything that makes dental treatment more bearable. In fact, it wasn't until my teeth were literally rotting away that I found a dentist who also used laughing gas, which helped blunt the terror enough that I could sit still in the chair, and eventually helped me overcome my fears entirely.
On my last dental visit, I was chatting with my dentist, who mentioned that they see many fewer cases of dental fear these days -- kids have grown up with faster drills and better anesthesia, not to mention better dental hygiene -- so dentists are seeing fewer problems, especially of people who put off treatment because of fear, which usually makes the problem worse.
So... unless you'd rather risk your daughter developing a phobia about dental treatment that could stay with her most of her life, I'd say don't withhold a beneficent support.
My experience with dental nitrous is according to my dentists, textbook classic. For me, it actually doesn't blunt the pain that much, but makes the FEAR reaction to the pain transient. More like "OWWWWW!... huh, that was intense. I wonder what he's doing next?"
I submit you can learn just as much from that experience, with less trauma, than with a painful, horrible, possibly agonizing session.