Warriors can be balanced at higher levels without Epic feats. It's just that warriors are currently more balanced as consistent survivors and damage dealers with reliable resources, rather than fragile mages that have their selective toolkit that is responsible for having the potential to fulfill a variety of roles, but not necessarily at the same time, or maybe not at all if they are not prepared. People may disagree about what inherent magic all warrior classes should have (magic being the only real way to explain supernatural attacks like shockwaves and air slashes and dragoon jumps).
I have no idea if Wizards will every explore the Book of Nine Swords-style magical warrior classes again. But there has got to be a market for it, right? If Wizards can't fit that into their tight design schedule for their 5-year plan, that is an opportunity for 3rd parties to get into that space.
The problem is though, in practice, this simply does not work.
Let's just take a snap shot at 11th level, the fighter will have let's say (10+4) + (11x6+4) = 124 base hp. They have 4 second winds, which will give them an additional 4x11+5.5 =66 hp. So, we can assume a daily hp pool of 190.
Let's say the average damage per fight for the Fighter is going to be something approximating the fire giant, a CR 9 creature. This is just to get rough numbers. We'll give the Fighter a greatsword, plate armor, and a magic item to increase AC, so he's sitting at 19 AC.
+11 on two hits per round, three rounds of combat per fight on average.
.65x28x2 = 36.4 per round
36.4 x 3 = 109.2 per fight
Well... this is a problem, isn't it? A fighter can't even last two fights in this scenario. Maybe Giant's are too strong? But let's increase the level of the fighter to 16th level.
That brings their hp to (10+4) + (16x6+4) = 174 + (4x16+5.5) = 260 effective Hp. So, an increase of 70 hp which will mean the fighter can now last 1 additional fight against our fire giants. But the fighter also gained... not much to change how they approach the fights either. They got three feats and the ability to action surge twice, but that is likely all still being in melee and swinging their weapon. After all, before getting to 11th level they already had three feats which they used to get what they wanted. These last three aren't going to be dramatically changing their play style.
Now, I'm sure I here the complaint "Well, the wizard at those levels only has 74 and 104 hp respectively! So they can't even survive as much as the fighter can!" Very true, and what do you think happens when the wizard drops to near death and has very low hp? The adventuring day ends. The party finds a way to retreat, OR the fighter takes on additional damage so that the wizard survives long enough to get through the adventuring day. We have the term "meat shield" for a reason after all. So the adventuring day ends when one member of the party reaches close to zero hp.
Now, between levels 11 and 16, what did the wizard gain? One 7th and one 8th level spell. And these are significant, because they can each end a fight or drastically change it. That is a Forcecage and a Dominate Monster. And before that the wizard had three 3rd, three 4th, two 5th and one 6th level spell, and by 3rd level spells you get things like Hypnotic PAttern, which can end even high level fights. So the wizard is sitting on the ability to end or dramatically shape NINE fights.
So, the wizard with their low hp but massive power is dictating the number of fights we go through, no matter what. Because the Fighter is defending them, and taking their share of the damage, so the adventuring day is continuing, and they are likely the major reason the fighter can go through more than a handful of fights and encounters before their HP is simply tapped as well.
And all of this assumes that we are getting more than 3 or 4 fights, which is not a good assumption, as we have long known that 5e games have not reached the 6 to 8 fights per day that was originally predicted. So any plan that has the Fighter or other martial breaking even in fight 6, 7, 8, 9 or 10 is fundamentally missing the point, because they are likely only going to get to fight #3 before the day is over.