The core of the elegance is that allows flexibility while maintaining balance. In prior editions you had a 1 item per slot rule. That created a lot of problems that encouraged focus on a small set of items and resulted in a huge number of items being ignored.
In some editions you'd find a bunch of rings you'd never use, in others you'd have a lot in the rule set that would never be picked by players or DMs to be included.
This happens just as bad with attunement. In our campaign at 6th level, there are already "hand me down" attunement items and soon, there will be items that nobody wants because their attunement slots are full.
Attunement did nothing for this issue except to propagate it in a different manner. Instead of limiting the number of rings, it limits the number of attuned and cool magic items.
And quite frankly, the "ring problem" still happens for some other items. Only one shield at at time, even in 5E. Only one set of armor at a time, even in 5E. Only one set of boots at a time, even in 5E.
Here, due to the recommended distributions and the mechanics, magic items should be distributed and diverse.
Again, no different than earlier editions that had magic item tables with percentiles for different items. Diversity is totally DM dependent and if rolling on a table, basically dice result dependent.
As for why a selection of 3 attuned items per PC is not arbitrary: Math and statistics. If you take the average number of magic items that should be found based upon recommended distributions, calculate the chances that magic items would be attuned based upon the percentage of entries on the item tables that are attuned, and spread it over 20 levels, the answer becomes obvious. Basically, there should be about 3 attuned items found per PC in a 20 level career.
Are you sure of this? Where are your actual numbers for this? This seems to be a claim without any hard data written down to support it.
Let's look at some data. The number and percentage of attunement (non-consumable) items in the DMG is as follows:
37 out of 83: Uncommon (45%)
56 out of 97: Rare (58%)
42 out of 65: Very Rare (65%)
31 out of 43: Legendary (72%)
160 out of 288: Total (56%)
So except in the case of uncommon items, a majority of non-consumable items require attunement.
Based on your assumptions with a party of 4 PCs, in 20 levels, those 4 PCs will find 100 / 56 * 3 * 4 = 21 magic items or 1 magic item total per level. 56% or 12 of these items will be attunement, 44% or 9 will not.
One magic item per level is a bit light, even for 5E. This, of course, does not even take into account crappy items being found (cursed, a magic mace when nobody in the party uses maces, etc.).
The real issue here is that tables B, C, and D are mostly consumable item tables in the DMG. So, the game is set up at low level that the PCs should be finding mostly consumable items, but if one looks at LMoP and other modules, that's not the case.
Personally, I think that players enjoy acquiring magic items as a major part of the fun and if it takes 5 or 6 gaming sessions to acquire level and only one magic item is found in that time frame, it's not as much fun. IMO.
The 3 limit encourages distribution amongst the party and limits the power of PCs that find too many attuned items - especially when there are too many high power attuned items. It prevents a party that finds too many items through luck, or a situation in which a DM allows PCs to buy items very easily, from getting too far from the balance levels that were envisioned for the game.
Actually, it does not limit the PCs from finding too many attuned items. Random is random. The DM could roll 14 attuned items out of 20 found (even including consumables).
That is the first level of analysis. I encourage you to think about it some more on your own and look for the deeper balance issues. I could write a few dozen pages on this - but long posts never do much good. People tend to only learn things during message board discussions when they figure it out themselves.
Hmmm. This last sentence is a bit condescending. As if people could not come to a different conclusion.
It's pretty obvious that WotC set up the tables to match their expectations, but at the same time, WotC is not playing the game. People are, and people often fudge those tables to get results that are more fun for their individual groups.