Fighters are a class for new players, or players who don't care as much about in combat options or character variation. That's not meant as a negative.
I'll accept that you don't mean it to be negative, but it is one reason people think fighters suck. Lack of options, simplicity that can potentially shade into boredom under the wrong circumstances, and a 'training wheels' label tend to get people to give up on the class rather than explore what they might be able to do with it - or ask for more/better options from the class.
"2.5," 3e, PF, 4e & Next all tried to add interest to the fighter, in the process, the Barbarian became the easiest class for a new player to tackle in 3e, and the Archer-Ranger took over that spot in 4e, then handed it back to the much simpler daily-less Slayer sub-class of Fighter in Essentials (which is very similar to the Champion, while the very similar Essentials Knight was closer to a Sentinel Battlemaster build).
5e at least splits out the Champion as the training-wheels fighter, removing some of that stigma from the class. It resorts to spells (EK) to make it interesting/versatile, though (with the Battlemaster in relative limbo between the two, complex for little payoff, but amenable to system mastery to optimize for DPR).
But, still doesn't suck. There's just a lot of design space left for more versatile/interesting alternatives.
most of their strongest features are attainable by level 2-3, making it far more rewarding to dip than to dedicate. This is actually their biggest problem, design wise: while the Champion is supposed to be as simple as possible, and the EK gets spells, the battlemaster really needed more fiddly bits to play around with.
Maneuvers gated by level, for instance, would have extend the shelf life of the Battlemaster. If some maneuvers gained at high level were genuinely better than those picked up at 3rd, that is, not just different.
As a player with almost 40 years under my belt, I second everything you just said here. I have always preferred fighters and other martial characters to spellcasters. ...
With that stated, I've been mostly playing Barbarians in 5E.
You're so satisfied with 5e fighters that you won't play one?
Combat options and variation are almost solely dependent on my imagination: how I want to role play the character, and ideas to use the environment to my advantage in a fight.
Your DM's opinion of the options your imagination comes up with can be a pretty profound limiter on that kind of thing, too. But, sure, if you have your DMs number, you can probably get away with quite a bit. You could do so with any class, really, and the more variety the class brings to the table, the more you can leverage that to try other imaginative variations. The advantage of the fighter in that regard is like that of the 'brick' in Champions! - you can improvise and try daring things because you're more likely to survive screwing them up (though, no subsequent fighter has ever quite lived up to the high-level AD&D fighter with his butch saving throw matrix when it comes to that).
I'll also say that the battlemaster is just complex as any other class.
Let's see. You choose 3 maneuvers, and choose how to spend CS dice to activate them between rests. You can't swap the maneuvers out and don't get new ones for a while. That seems significantly less complex than a 1st level neo-Vancian caster. And, the Battlemaster never opens up new & improved maneuvers as he levels, while the neo-Vancian caster does so ever other level, he just picks from the slowly shrinking list of maneuvers that were balanced for use at 3rd level. Not spectacular. I think there's still an assumption of simplicity being desirable, even for the Battlemaster. That said, it does plenty of damage, and can blow it's CS dice and Action Surge to nova something fierce, so it's not without effectiveness, and a bit of resource management.
Still doesn't suck.