So the other element is player expectations. Me— I personally might because I tend to expect those things, having played many TTRPGs. My daughter, who has no such experiential baggage, might not.
Back to HP, I’m not an expert on the lore but, generally, all the wands are interchangeable, right? Other than the three master wands or whatever they’re called. So in that case, a wand, like a mundane tool, might not need stats/mechanics.
Ultimately, it’ll be on you to set up the context and sell the players on the concept to overcome any expectations.
I think a lot of things in HP are only half-baked but that’s just me.