I mean, none of that answers any of my major points, so I guess you don't disagree with the rest of them. At best Bladesinger is not quite as bad, name-wise as PDK (the main problem is really the "Purple", it's so lame). But it's from the same book, has the same issue (if to a lesser degree) and is #1, rather than what, dead last?
I wasn't going to address every point you made for the sake of brevity so I chose the ones I thought were the most important.
To address your other points briefly: Yes, being least popular doesn't mean it's unpopular. Those have two separate meanings. The reason it's brought up is because the arguments usually starts with how people hate this, that, or another while that's not what the polls gave. It wasn't an unpopularity poll, it was a popularity poll. It's the difference with movies being on the bottom of my "favorite movies to-watch list" and movies being in my "least favorite movies to watch" list.
Isolating it to players that have all options available still runs into the issue that the most favorite options are the free ones. The free ones are iconic and familiar and most players who bought the other options also played with the free ones beforehand.
Maybe a more interesting point can be found with unpopular vs. least popular. When people are only picking one thing, it doesn't really matter if something is "unpopular" or not, if it's still the least popular. And whilst I doubt PDK is popular, you do get this thing - it happens with books, movies, even people, where people say that they like them, but, when it comes down to the picking, that kid is still last for your team. And so you can say "Well Timmy is a nice guy and everyone likes him, look I did a poll!" but when Timmy is picked last for dodgeball every single time, even though he is well-liked, you gotta look at why that is.
Turns out Timmy has terrible reflexes and can't throw to save his life, and when it comes down to it, people pick everyone before him. He's a cool guy, but that's not good enough.
PDK is the worse version of Timmy. Tarquin. He's got a stupid name (sorry Tarquins of the world...). He's not particularly popular. And on top of that, he's not at all good at dodgeball. That's why he gets picked last.
Both of our metaphors fall flat in this instance anyways. It's not like an election where there's only 2 options and it's not like a basketball pick where everyone has to even participate. The dragon knight isn't being voted into office against a Champion, they can coexist together. At the same time, the PDK isn't
required to be put in, along with the other fighter subclasses. No party even requires a fighter in the first place.
But let's take it as it is. The percentage of those who played a fighter that chose a Purple Dragon Knight. This could mean that a wide range of players tried it once and never again (Bad experiences, uninteresting, etc.) Or it could mean that only a few players tried it and many of them continuously play them (fun for those who tried).
Let me be clear, I never played PDK at all. I've seen the features and they don't seem weak, they just seem like something I'm not interested in as a fighter. Whether the subclass is good or not in play isn't something I can opine, but I can say that just because something was on the bottom of the "most played fighter" class doesn't make it bad.
That same survey puts fighters more than double the popularity of a Druid and wizards are middle of the pack. That doesn't necessarily make wizards a mediocre class or druids a bad class.