Hiya.
IMHO, your players are whining because they feel like something has been "taken away" from them. Now, if your players didn't grow up playing 3e/4e or PF, then they are likely just not used to the restriction because in 1e/2e you could have a whole bag of holding worth of magic items. Then again...magic items were in the "really nice to have, but not necessary". But if they
did grow up playing 3e/4e or PF...
...then, as I said, they are probably feeling like you just took away their toy box and are now acting out in an effort to get their way. As I've always said, it's
always easier to give something to players than to take it away. The designers of 5e saw this too (I hope!), because they put in Feats and Multiclassing as
optional rules. Meaning that if the DM says "Yeah, sure, we'll use Feats this time around", then the players see it as "getting something" rather than the DM saying no to them and the players thinking the DM is "taking their stuff". Magic-Item Attunement is kinda the same thing in 5e.
5e is based on "
no magic items needed". So, any magic item the PC's get are, truely, actual
bonuses. It's like going through a drive through, paying for your meal, and finding out you got an extra apple pie in the bag. You didn't pay for it, and it wasn't assumed...it was an actual
bonus.
Now, that said, the designers obviously figured magic items will play into just about every D&D game simply because going in to dungeons and fighting dragons
should give you treasure...including magic items. That's been kinda the point of the game since the mid 70's; go into a dungeon, survive, get treasure. Of course, they also know they had to deal with the magic item problem that 3e/4e/PF has; the "magic item for every situation" problem. Especially when a PC can just up an make them or is assumed to be able to just go an buy whatever he wants. Given enough money and resources, just about anything can be accomplished. Like, say, take over a small country. The three item attunement limit is there
specifically because of this. Because magic items are, generally, not "assumed"...but they are kept in mind... the rules need some way to give DM's a worst case scenario when they are designing dungeons, planning governments, and terraforming continents for their players to explore and engage in.
The more "attunement" you let your PC's have, the more out of whack your game
will become. I guarantee that. You will start playing the Final Fantasy "one upmanship" game. The PC's can pump out 40% more damage per round...you need to up the challenge by 40%. They counter with an increase of 20% in defenses...you counter with 20% in offense.. They enhance mobility by 25%...you counter with things that decrease their mobility by 25%. Basically, you and them start getting frustrated because all this "work" is pointless and nothing is being gained other than having you and your players feeling of "Ah-ha! I can use my Magic Item of Wowzerness here!" reduced to "Oh...I would use my Magic Item of Wowzerness here, but what's the friggen point...something will nix it or make it useless anyway...may as well just attack. yay.".
I've also said in other threads.... RPG's (most, especially D&D) is a "zero-sum game". Nothing the players do in terms of builds, items, and all that other "optimization stuff" is going to do much to any well-run campaign. The only thing a player gets from spending 9 hours trying to design the "perfect build" is enjoyment out of reading rules and trying to puzzle together bonuses and stuff. After a short (very short) time in the spotlight doing his "build thing", the campaign will start to even out the playing field with other things. Either direct counters to the builds OP'ness, or things in the campaign where the OP'ness is either ineffective/pointless, or becomes an actual detriment.
Now that I've rambled on for quite a while... the "Proficiency bonus +1" option someone posted above is something I'd do if I really had to (which I wouldn't; I'm kind of a hard-azz DM and well known for being stingy with money and magic in my games...but I've kept the same players for 20 and 30 years, so I must be doing something right!

). Telling the players they can have Prof bonus +1 Attuned magic items isnt' taking anything away...its giving stuff to them. Players like that. It also doesn't get crazy. Just remember...if they still keep complaining, stick to your guns! If it starts to get to a head where they are harping on it constantly...tell them one of
them can take over DM'ing for the next 8 months and then they can do whatever they want.
^_^
Paul L. Ming