I think what you are saying is that you do not agree with the designers' power ranking of items. Some items that you feel are powerful enough to need attunement, don't. Other items that you find weak in play, do. It is interesting, but I think you'll agree irrelevant, that you would characterise readings that agree with yours as "careful"
Let's call your objection one to "uneven handling".
I suspect that there are very few people who carefully read the list of DMG attunement items who think that every single one belongs on the list.
As an example, in a campaign that revolves around the ocean or a large lake, a Trident of Fish Command has some utility.
In most campaigns, it has a lot less utility than a +1 magic weapon which does not require attunement (considering that the +1 magic weapon is +1 to hit and +1 damage, and the Trident of Fish Command is not).
Ditto for a Brooch of Shielding. Sure, if the DM throws spell casters with Magic Missile at the PCs right and left, the item has some utility. It's practically worthless otherwise. There are dozens of attunement items that most players would want over this.
In the case of uneven handling it is not going to be sufficient to just increase the number of permitted attunements. As some items will still use up that capacity that shouldn't, while others will not count against it but should. Of the replies to this thread I have read, I really felt that CapnZapp was thoughtful. It touched on something that Unwise echoes and that seems simply obvious once you reflect on it: at different times in different campaigns, the effective power level of an item will differ. Ergo, uneven handling is inevitable as it relates to perspective.
Given a large enough number of allowed attunement items per PC, uneven handling is not an issue. But with 3, it can easily become an issue.
Given the inevitability of uneven handling due to the wide variety of perspectives, we would need a system that calibrates against perspective. This would be a matrix similar to that proposed by CapnZapp but further subdivided by your campaign magic level per the table in the DMG. Even then it wouldn't please everyone, but I think it could go a long way toward meeting your requirements. Thus a +1 sword could require attunement by a low-level character in a low magic campaign, but not otherwise. Unfortunately, an uneven handling objection can never be answered completely because for example I find +1 stat items powerful whereas you don't. A party's ability to pass around an item that ticks characters up to the next bonus makes a big difference in skill-use heavy campaigns like mine for many of the same reasons a +1 sword can make a big difference in combat-heavy campaigns (I'm not saying yours is of course, just that it could be a context in which a +1 sword could feel better than a +1 ST).
It also is dependent on how the DM handles skills.
If 5 PCs can roll the skill and a single success is sufficient to accomplish a goal, than an item that can be passed around means little for the vast majority of skill checks. For example, +1 to +4 to one of 5 rolls from one of 6 ability scores with an average 30% chance of success per PC without the item decreases the average of failure from 16.8% without the item to 15.6% to 12%. That's an increase of success for the group of 1.2% to 4.8% depending on which PC gets the item. That's mostly white noise.
If only one PC can roll the skill, then a +1 to +4 can help. But, it has to be the PC that has the item AND it has to be a skill for which the item helps. Again, a bit rare, even in a skill heavy game.
Ditto for saving throws for many such items. There are extremely few Int saving throws in the game, so a a bonus of +1 to +4 for Headband of Intellect almost never helps in the game for saves. And for spells that target AC, the item is less helpful than a +1 weapon (which does not require attunement) is for a melee combatant.
Granted, I do agree that items that boost a stat to 19 are worth attunement. I just think that there are other attunment items that are a lot more useful (and others that are a lot less useful).
