Bandana Waddle Dee will always be that random nobody that just as randomly became a somebody for no true reason to me.
I don't have any real issue with him, but he's just....why is he even a big deal now to begin with.....?
The one thing think you need to understand first is that Kirby fandom. To demonstrate a point. Let's talk about this guy:
His name is plugg. That really isn't something me or any of the kirby fans should really know. After all he is just a random enemy and not even really an important one like Goombas or Waddle Dees. But people certainly learned of him quickly when it was revealed he would be in Star Allies. All that is really special about him is that he was an enemy from Kirby 64 and he is cute. But he quickly grew in popularity. People got attached to the little guy.
I guess what I'm trying to say is that people get really attached to the characters of the kirby series. Even if they had a minor role or something like that. And that's important to understand why Bandana Waddle Dee was popular.
Now one thing I can say for certain is that Bandana Dee started becoming popular before smash 4 was announced. So it wasn't the idea of getting a kirby character into smash. I should know because I started liking him sometime before smash 4 was announced as well.
I feel like it was a mix of three things.
1. He became a playable character.
2. Him being a Waddle Dee
3. His role in Super Star Ultra.
The first may not seem like much based on what you are saying. You are right, he was a random pick for the 4th player spot...but it was still the 4th player spot along with Kirby, Meta Knight, and King dedede. It doesn't matter if he deserved it or not, just by the sake of him being there meant he did. Because kirby fans get really attached to the characters. And people started obsession over it.
The second thing was of course that he was a Waddle dee. The kirby fandom is obsess with the idea of cute things. After all that is a major thing that sets it a part from other franchises. It's consistant cuteness. Which of course makes the nightmareish abomination at the end of kirby games more special. And Waddle Dees are cute. They consistantly get involed in cute things. Wheather it is them driving cars or being lumberjacks. And also Epic Yarn.
The third was probably the actual spark though. When he was confirmed playable, naturally everyone wants to know all they can about him then. And what do you remember/learn with that? That he had a role in Super Star Ultra. Suddenly Super Star Ultra became more special of a remake. I mean wow they are actually referencing the remake. And a reference to one of the best parts of it being where masked dedede got his origins.
And continuing to look at it, you see they actually gave him a character. He's weak, but he wants to help out the king. And speaking of, would you look at that he was playable along side the king. A connection was there. And with all that people ran with it. Bandana Dee became a very special character to the kirby fandom.
I feel like a lot of it actually has to do with how Kirby super star ultra kept getting reference. Bandana Dee, Galacta Knight, Heavy lobster's music, and another Soul appeared in that game. Continuity like that felt very special.