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There are a number of things wrong here.
First off, the fact that some people, maybe a large number want a simple fighting option does not mean all expressions of the Fighter even within a given edition have to be simple. As I understand it, 5e does subclasses; you can have the most basic subclass be dirt simple to play, and still have others than have some nuance. You just have to want to bother. To what degree that is or isn't true I'm unqualified to say.
Secondly, expecting people to believe what WOTC claims about their surveys reaches well beyond any issues anyone has with any given class. It requires you to assume that WOTC is, to be blunt, a lot better and more coherent in their survey methodology and assessment that a number of much bigger companies have shown themselves to be over the years. So lack of faith in that can be entirely orthogonal to what one feels about any given decision there.
Finally, when you're talking about the kind of data present here, I'm going to stand by the opinion people are making a large number of assumptions and jumping to conclusions on what is, at best, a very limited chunk of data that has a lot of things that need to be accounted for. I'd have exactly the same response if there appeared to be a number of factors that seemed prone to, say, stating no one played rogues, because it would be bad use of the data fueled by people's desire for it to say something they wanted.
As you note yourself, I'm not a 5e person; my actual interest in the 5e base's real feelings about their Fighter as constructed is limited because I'd have to care more about 5e in general. But I do care about people jumping to conclusions and reading more into data than is there, so if someone wants to claim my reaction to this is my agenda about Fighters talking, I'm going to reserve the right to roll my eyes. If you want to aim that gun, aim it at 5e people who have an issue with the 5e Fighter, not me.
In no particular order-
The reason I noted that you don't play 5e is not because you are not allowed to discuss 5e. It's for a more salient reason- while you might think that your lack of playing 5e somehow makes you more dispassionate or a better observer or something with regard to this conversation (about the statistics of people playing 5e), others might view it as odd. Because ... you are very invested in a conversation over which you have no first-hand knowledge. Other than observing the comments on these boards, which are not representative of the player base as a whole, you really can't speak to the issues that people keep telling you. So when people (as they always do) keep saying that there is a high demand for the "simple fighter," especially for new players, it is bizarre that you choose to push back so hard given that you don't actually have any knowledge at all. Again, since 2015 I have run games for new players, repeatedly, for years, and the fighter is the single most popular choice, over and over again, over the course of years. These are players that are new to D&D, so it's not like they've been "contaminated" with past edition knowledge. And this anecdotal experience matches with the anecdotal experience of other people with similar experiences that I have spoken to. Moreover, it matches with the stats that are reported.
Next, you complain about the data set. Again, we see the same thing here that we have seen
every single time a data set is reported. The fighter comes out as the top choice. And the same thing happens- people recognize that the stats broadly match what they are seeing, yet some people choose the release of data set (again, this isn't the first one!) to choose to go on a "fighters are too simple" campaign. This would be similar to a company announcing their most purchased product, and instead of people questioning the other products, a small group of people immediately starts saying that the most purchased product is, in fact, the one that most needs to be changed to suit their own personal preferences. It would be interesting if, instead of demanding that the people who are reading the data (which is in accord with the data that has been released over time) to say exactly what it says- that the fighter is the most popular class, and that this is what they see when they play the game, you might actually be a little more critical of those who are actually leaping to conclusions that are not based in the data- you know, that while the data continually shows that fighters are the most popular character, this is actually evidence that supports their a priori belief that fighters are the class that needs a serious re-design.
Finally, I am not going to further address your issues with WoTC's survey methodology. There has been enough ink spilled on the issue of their choice to design in a "safe" manner by only making broadly popular changes. It is what it is; that said, I don't particularly care to go down the rabbit hole of those who will often criticize WoTC for "slavishly following surveys" and refusing to make bold choices on the one hand, and then criticizing WoTC for not correctly using data on the other hand.
All that said, I don't think that
all expressions of a MARTIAL character need to be simple. I do think that there is a cap on the level of complexity of the
fighter; the Battlemaster is about as complex as a (non-spellcasting) fighter can get. Since you don't play 5e, I don't know how familiar you are with this, but the amount of additional complexity a
subclass can introduce is somewhat limited. The Monk, a class I enjoy playing but has its share of issues, is a more complex martial character. I'm sure that they could work on designing a more
complex martial class and I wouldn't have any issues with that- I think it would be great for those who desire it. I wouldn't want to see that in the base fighter, because, again, there is a strong demand for the simple martial*. A lot of people learning the ropes of D&D like to play it. And a lot of veterans who just want to relax and hit things also enjoy it. It fills a needed niche for both on-boarding and allowing a group of people to play the game they way they want to- which has been born out not just by this data, but by the data we've been seeing repeatedly for years, as well as what you would see if you played the game.
The issue with bringing in a complex martial character class, of course, obvious. First is the design decision to imbue complexity through spells. Martial characters such as the Paladin and the Ranger were given spells to provide them "abilities" and "complexity," and 5e basically punted on the idea of additional martial complexity
qua martial abilities. You have the Monk and the Battlemaster, but introducing a class with its own complex tactical martial abilities runs into the same problem that we've seen with psionics- the introduction of a new system, and the fact that it is only supported by a minority of players who have competing desires.
I want people to get what they want, always. But part of that is being realistic about why things are the way they are. I am looking forward to WoTC releasing a new, low-magic Greyhawk that has no bards and elves. But I'm not holding my breath.
*Arguably, one issue with 5e is that while the Barbarian is differentiated from the Fighter in that it is the "tanky" class, they both occupy the "simple martial" area.