Then we cannot, from "popular," reason that things are well-liked. Just that they are common.
Yes we can because even though they are universally available, they are also other options available and they chose fighter over those options and that is after the choice to play the game at all.
With that being the case, I find it reasonable to believe that the fighter mechanics are more "well-liked" than mechanics of other universally available classes.
Okay, but what does "many" mean? If a thousand people like it, is that "popular" when millions of people now play D&D?
Yes clearly.
If a million people play it without regard for its mechanics, can we reason from its "popularity" to say that therefore people absolutely adore its mechanics and changing them in even the slightest degree is super ultra mega bad never ever ever do that?
I don't reason that from this survey. I reason that from many games I have played in, my own feelings and many other players I have played with.
This forum is the ONLY place I have interacted with any people at all who have expressed dislike for the fighter class mechanics and even here I am not sure it is a majority that dislike it.
For that reason, I believe that the vast majority of players do in fact like the mechanics of the fighter class as they currently are.
Fighters have been commonly used in every edition. Yet, as I have said--and again, not one person has disagreed with me--the 3e Fighter, which was extremely commonly used, is widely regarded even by 3e fans as a poorly-designed class. Hence, poor design is not enough to make people avoid the Fighter. (Edit: Okay, I hadn't seen it yet, but Lanefan has slightly disputed it.)
I did not play 3E enough to have a valid opinion on the subject.
I will say from personal experience, many people disagree with you about the 5E fighter though.
You want me to prove that I believe something? What can I offer you as proof of my beliefs - will a video of me swearing on a bible suffice?
I have been careful to explicitly state my opinions as opinions. Meanwhile you state things as facts, or at least definitive statements and offer no proof at all.
Before you ask about proof of my beliefs, you should provide some proof of what you are suggesting?