And here is the key. It doesn't matter if other classes aren't meant to use spells, headband allow it by min-maxing. Which is OK, but it is also OK to ask for equivalent equipment for wizrds to balance things out. Also, magic missile is not that good. After all, average damage is 10.5 damage points. So at most you would have 4 in a combat. Then rest. On the other hand, rogue can have infinite backstabs. At Dexterity 18, using +1 weapon, it is easy that they have 5+1d8+1d6 damage each attack, average 13. And that is, of course, if they don't use venoms or other nasty stuff. So even if you duplicate the magic missiles, damage wise, the arcane trickster is more effective. And that is even before we take into account the "hide" cheese move. You can effectively solo the game as a rogue arcane trickster. Which granted, is the same as BG1. And there is even some boots of speed there. XD
You can min/max without it. A half elf can get 16 in any 2 stats,14 in con, plus 16 charisma. Thief is better than an arcane trickster anyways. I fixed the thief not be able to get lvl 4 wizard/cleric/warlock feat. With that, have the necklace with 1d4 psychic dmg with magic missile , +2 offhand attacks. 1d4+1 x6
Or you could get Warlock feat at lvl 4, throw out hex and get 1d6 for 3 hits per round , if you have advantage sneak attack on top of that. And with 16 charisma, your eldritch blast is quite accurate also infinite.
There's no need for the headband. Plus SHADOW OF MENZOBERRANZAN is better for solo.