The sense that I take from these statements is that magic items should all be interesting and unique, and an item +1 cheapens magic to just another game stat.
I agree in general with the sentiment. Magic should be unique and interesting! So what I used to do, back in high school, was never to give out any magical item unless I had carefully placed it in my dungeon. I remember the party was once forced to fight a demon that was harmed only by magical weapons with the single Dagger +1, which I had placed in a dungeon somewhere elsewhere ...
... one of the players was later so desperate for magic that other players (okay, I was one of them that session) played a joke on him by casting continual flame on a quiver of arrows and making them seem like some kind of flaming arrow.
Sure, you're right--that Dagger +1, even though it was the only magic item held by a party of 6 or so ~4th level characters, didn't actually have a name or anything. It was still just an item +1 ... but its magic still made that encounter more interesting ...
|"So help me if this is just some Sword +1, +3 versus Undead!"|
So I agree with the general sentiment, that magic items should be unique and interesting, but I disagree with the practical idea that one should not include "generic rulebook stuff". How to make this jive?
First, what's the motivation to cut out the generic item +1? Is it for the players or for the referee? In every game I've run, players are always happy to run across the next Sword +1 or Shield +1 or whatever. Even if they don't immediately use it, they can add it to their "downtime" inventory, they can give it to a favored hireling, or just hold onto it to bribe the dragon instead of using their personal Sword +3 of Whatever Awesomeness.
Likewise, as a player, I'm happy to pick up extra items +1 to add to my inventory for use by my henchmen/hirelings--or, at first level, it's just fucking awesome to finally have a magic thing!
As a corollary ... sometimes I as a player just don't want a weird magic item ... I know, I know, "weaponize floating disc and mending" and all that, and use every item in weird ways, but still, sometimes I just don't see a use for the thing. Maybe someone else does--and I'll be glad to give it to them! But sometimes a Sword +1 would just be kind of generically useful ...
Second, assuming unique magic items is a thing for the referee ... you don't need every item to be magically unique to give a unique description to the item. A Sword +1 can be a sword "marked with the maker's mark of the Waterfall", or it can be a "narrow grey sword with weird Dwarvish runes", or it can be "a flashing scimitar with a spider hilt", etc. etc. etc.
I have some specific traditions of magic-sword forgings in my game that provide ready descriptions for otherwise generic swords. I need more such, surely; and I need the same for other "generic" magic items that could be found in the game; but I've gotten by so far with what I have ...
Third, the randomness of the tables in the book is a large part of the appeal. I had a dungeon that included a staff of power in one of the rooms on the first level because I rolled the 01 on percentile dice for a magic item present, unguarded (likelihood 1%!), and proceeded to roll within 91-95 (Wand/Staff/Rod), and then 22-23 (Staff of Power). Honest rolls. Which meant, when my players found it, that they had a staff of power! Its use was their prerogative ... only just now, six years later, have they finally "used it up". Without rolling it, there's no way in hell I would have placed it there--but with random generation ... well, sometimes adventurers get lucky!
Corollary to that--if you don't like the generic tables, write your own tables specific to your setting. I keep intending to do this for myself ... but really, I have no beef with items +1 (and I don't want to spend the time). My players eat them up. I generally have handy descriptions for them to differentiate one from the next (eh, I sometimes do). Too many?--items get lost. And even the generic magic item tables have a variety of interesting things that players have never seen, or have rarely really gotten a chance to play around with, session after session (Blackleaf in my Greyhame Game has a medallion of ESP 30'. It's the first time for me as a referee ... after 20ish years of D&D? ... to have to deal with it--and definitely the first time for her as a player of maybe five years. She abuses it at every door, and I roll with it ... someday there'll be a monster with an amulet of protection from ESP ... rolled randomly, of course)
So call me a conservative in this regard, but I'm fine with a Mace +1 (its head is fashioned to resemble elephants with mighty tusks) and a Ring of Protection +1 (where a stone would be set instead is a piece of a saint's fingerbone). I'll place super-special magic-items here and there in the dungeon where I will, but for any old hoard (and a dungeon-level should hold several), I'll roll randomly just to see what shows up.