Condolences on the loss. My Dbacks lost last night, as well, though we weren't at the game since they're in St. Louis. Our #2 pitcher got hit in the head by a liner, but he's apparently okay, thankfully.
Carrie is extremely social and talks to just about everyone, but I'm sad to say I've never observed her having such a braces-centric conversation with another person in braces. She's had many (dozens, probably) convos with family, friends and acquaintances about her braces, why she got them, etc. But those have mainly been brief, as most people only care superficially, and the talk moves on to other subjects quickly.
The only somewhat lengthy convo I've observed was with a friend of ours who is a dental hygienist who also recently did Clear Correct (Invisalign knockoff). She had an above-average interest in Carrie's braces, for obvious reasons, but it wasn't anything like what you and your wife experienced. I can only wish!