Cautiously like. And I think the limit of 3 is fine... except that I'd add a feat to expand that limit and give the Artificer a class feature that exceeds it (if they ever do an Artificer class, of course!).
I like it in principle. I think the limit of three is fine as a base. It definitely works in terms of preventing the magic item Christmas tree effect from past editions. However, as someone who is playing a 20th level PC, I think it would've been nice if they'd included an epic boon in the DMG that let you attune to a fourth item. It doesn't seem all that OP at that level.
I also agree that there are maybe a few items that require attunement that shouldn't (and maybe some that should but don't).
I like it - not really relevant in my low-magic Wilderlands campaign, but now I'm running a Pathfinder AP in high-magic Golarion it's a good way to keep items under control. After the first book of the Shattered Star AP some of the PCs already have 3 attuned items each, the limit is a good way to give out items without things going crazy, and not have to worry too much about stacking - eg I can give out multiple AC-boosting items, and as long as they require attunement there's no need for 3e/PF style 'insight' 'morale' etc bonus types. Players can simply take the best ones and sell or redistribute the others. I can even allow some item purchase, likewise.
It solves a lot of problems that plague 3e/PF, a lot more elegantly than 4e.
I certainly wouldn't change it.
I like it - it balances magic items with game play in 5e. Of course, your DM can always house rule if you want a higher magic quotient. You just need to adjust the CR of your encounters accordingly. That's the most impressive part of 5e to me. Core rules are very well balanced across most rules, plus it is easy to expand and adapt to fit you and your group's play style.
There was an interesting optional rule during the playtest that tied the number of attuned items to your Charisma modifier. I incorporated a modified version of that in my current campaign, where you could attune 2+modifier items. I thought this would be a good way to keep players from toileting charisma (which is fairly common, IME).
However, with 5E's glut of Cha based spellcasters, this isn't the case, and all it's done it encourage players to play concepts that use Cha as a primary or secondary ability. It was a good idea in theory, but I'm probably going to drop it for my next campaign.
I like the attunement rules, and I'm totally on board with the 3 item limit. But then, I run low-magic games for the most part.
Look at it this way: Bilbo Baggins ended up with two magic items: a ring and a sword, plus he had some elven chain. All were incredibly rare and valuable and he passed them down to his family when he got older and had one.
That is the kind of benchmark I use when creating/utilizing/distributing magic items in my campaigns. Magic items are rare and significant. The attunement/limit really just provides a mechanical backup for the approach I take anyway.
I'm ok with keeping a lid on magic items with the 3 attunements rule, though it does feel a bit odd from a roleplaying and fantasy perspective. "Sorry, Gandalf, you can be attuned to your staff, robe, and cloak, but not your scarf. Or your hat. That's too many. Laws of magic, or something, I guess."
Thr idea of tying the number of attunements to a stat is intriguing. What if it was tied to a character's lowest stat? Perhaps something like 3 + lowest stat modifier?