I hit up on this idea a few minutes ago, so I haven't had much time to think about it. However, I think that attunement may disproportionately impact martials, and one possible solution could be to remove attunement from most martial oriented items.
Some background. As a result of this thread, I've been thinking a lot about how martials, even dating back all the way to the origins of the game, were kind of wuxia/superhero. It was simply silo'd into magic items.
Some examples. Boots of Springing and Striding that allow you to move and leap like a character from a wuxia film, doubling your movement and allowing leaps 15' high and 30' long. Or a Sword of Sharpness/Vorpal Sword, which could decapitate an opponent in a single strike (if you rolled well). Or the Hammer of Thunderbolts which, if paired with Gauntlets of Ogre Power and a Girdle of Giant Strength would basically make you Thor (more on this later). I could go one for pages, but hopefully you see what I'm saying.
For anyone who might not be aware, the original magic item tables were significantly weighted towards martial items. It was part of the balance of the game. Martial characters needed to have certain magical gear, without which they could be rendered largely impotent. For example, there were quite a number of monsters that couldn't be harmed unless you had a +x quality weapon, or otherwise used magic. I don't recall resistance being a thing back then; it was pretty much all or nothing in most cases. The magic items tables made it so that that finding such gear was likely, and finding gear for casters was relatively unlikely. There was a certain degree of 'easy come, easy go' mentality, in that there were many ways in which magic items could be destroyed, but by and large they were meant to be acquired and martials were meant to have the lion's share.
In 3e, wealth by level was introduced, wherein all characters were expected by the system to have a certain amount of magical gear. This meant that martials no longer got the lion's share of the magical gear, and that everyone was expected to have (presumably) equitable magic gear. In my opinion, this was one of the biggest buffs that casters received in any addition, and from what I can tell it flew under the radar for a lot of people. It also lead to what has been termed the Christmas Tree effect, where high level characters would be blinged out in magic gear, from head to toe.
Bear with me, we've almost come full circle to my opening statement. 5e, as best as I can determine, retained the idea that everyone gets magic items, but reined in the Christmas Tree effect by only allowing 3 attunement slots. Casters are far less reliant than martials on magic items, having spells that allow them to make up for deficiencies (they can also make up for martial deficiencies).
I was looking at the Hammer of Thunderbolts in the 5e DMG, and I realized that in order to attune to it you need to use all 3 of your attunement slots! One for the Hammer, one for the Belt of Giant Strength, and one for Gauntlets of Ogre Power. That leaves no room for attuned items that address the martial's deficiencies, such as Boots of Springing and Striding, or Winged Boots. And this lead me to realize that attunement really holds martials back, because high level martials need magic items to compete on the same field as casters. A melee martial with no magic that allows them to fly is going to be ineffective against flying opponents. A melee martial with no magic is going to be useless against monsters with immunity to non-magical weapons. So on and so forth.
As such, I think one way to improve martials would be to significantly increase or even remove the attunement limit for martial characters. As I've said before, siloing effectiveness for certain classes into magic items is not my preference. I would prefer to have it baked in to the class itself. But, that aside, I'm currently of the opinion that attunement limits martials a lot more than it limits casters.