Thank you for sharing your experience - and I agree with you that it's definitely an iconic item. Your analysis was quite convincing. My main concern is about too powerful for level 7 or not...
First time post, long time lurker, but had to weigh in.
My party is playing PotA and we had found a wand of fireballs at around level 6, so one level earlier than your party. I can safely say as a phoenix sorcerer that it did not feel in any way overpowered or that it made things way too easy. The wand made its journey through a few party members until I got it (we talked about how it was stepping toes on the flavor and role of the phoenix sorcerer) and it was more iconic and awesome feeling than anything else.
Did it trivialize or make it easier on some minor mook fights or boss minions? Yep. It helped extend the casting power of the sorcerer quite a bit too. However, there is still a ton of resource management and drain and it certainly hasn't made the module feel any less dangerous or a breeze. There are still things to take into account such as friendly fire (a little less problematic on the wand of lightning bolt to be sure), but all it takes is just making sure things don't line up too often. Do it enough so that they get mileage out of it, but there is nothing better than having that feeling of getting one such wand and using it as a player effectively. The first time I got to use the wand, the party was ambushing 6 or so things and a well placed fireball inside the room incinerated 3 of them and the rest just surrendered letting us get some information. It was the most useful feeling ever.
Also, it could add another layer of RP, enemies facing such "destructive" or unexpected power of someone flinging more than 1 lightning bolt might retreat more often, regroup, get more help, get lightning resistance potions, etc.
We're now level 9 and it's already starting to "drop off" in power. Things are no longer dying to 1 fireball, are making their saves more often, counterspells are more plentiful, enemies are smarter and positioning better. It still helps in the resource management part, and it certainly is very useful, but as HP grows and dex saves start getting better, resistant monsters/enemies come along, it becomes less and less a "game changer". I'd say in my experience (I've gotten such a wand in 3 games so far at levels 6-8) that it's only really a huge game changer for those levels and after level 9 it's impact is a lot less than you'd expect.
Also for all the talk of giving it to a class who can't cast those spells - I'd disagree based on RP. For example, why bother taking fireball on a wizard or sorcerer if the bard or cleric can cast it way more often per day with that wand. It made me personally just not bother with the spell for a while and did other things because someone else can just fling that fireball and I'll just save 3rd level spells for counterspells. It certainly felt like some part of the character was taken for sure.