I actually think less variety in the early levels can be great.
Let's say the first actual +1 magic weapon you get is the Sorrow, and you don't find any common weapons like Longsword +1 or Greatsword +1 yet. The fighter of the party picks up the Polearm Master feat at level 4 because of this weapon. That itself is a story, how the Druids gave it to her as a gift after rescuing Halsin and saving the Grove, and how she learned to master it. (And lets remove that 1dmg per hit from Sorrow. It's so crippling no one will ever use this flavorful weapon. It's enough to have flavor text of "emitting sorrow" on the weapon. Not every detail has to be underlined with clumsy mechanical properties. Sometimes it can just be story and flavor to evoke imagination).
If every PC in the party is loaded with +1 weapons and a bunch of weird conditional items, the coolness and uniqueness of a weapon like Sorrow that has a story is lost in the noise of Sparky Sparkslippers and Protecty Head-Helmets with "if you Jump and Dash on the same turn, you get a Lightning Charge and Disengage against Large Creatures".
If you get an even distribution of magic weapons of all sorts, magic items are no longer a story. It's just gear. You don't make choices based on the items, you get items based on your preference. Magic items are not special anymore, they're mundane. Larian are quickly progressing towards making magic items mundane in BG3.
And at higher levels everyone will obviously have all sorts of magic gear anyway. It would be good to separate the low levels where you are starved of items and the high levels where you do have choice. That's one contributor to making your character feel like they have progressed. And even at high levels, choice should still exist between +2 this or +3 that, instead of getting everything you want at +3, conveniently from vendors. If you give players everything they want, magic items become mundane gear again. If you don't give players everything they want, you keep alive the thrill of adventuring and finding that awesome weapon in the next dungeon. You should never buy your best gear from vendors. If it's so amazing, why would anyone sell it in the first place?
Just to mention, none of what I'm saying is meant to defend the odd conditional items. They were a misstep, in my opinion.
That said, your point about a limited number of items is well taken. I think that would work incredibly well for the first playthrough. Unfortunately, I don't think it has as much replayability. Once the players know, for instance, that the only magic weapon is Sorrow, then they start to build around that from the start.
